I guess it is an as good as any moment for that post which has been percolating for a while and answer all of the above at the same time:
So. War of Heroes ending, Nemesis dead. The Elites properly surrendered. Given how forgiving Rhea is while being in Seiros Mode, unless someone tells me she how her behavior in that opening and Crimson Flower is the one of someone totally eager to accept surrenders, I am fairly sure it was a Cichol, Indech thing (was Wilhelm even still alive by that point), probably on the grounds of keeping something of their fallen brethren's legacy alive (what else are you gonna say to Seiros mode Rhea to make her spare her Mommy's killer's lieutenants?), with Machuil leaving out of disgust (it has to have happened, and sparing Nemesis' cronies is the likeliest moment for that).
Here it is, war won, Fodlan approaching peace. A peace and an order that Rhea/Seiros wants to see enforced in the future, pretty much durably. Since Adrestia is the one doing the political control, and that she cannot exactly wrest political control at that point. So the soft power approach (mainly) it will be. Archibishop of Foldan's faith. Look at popes in medieval times to see the means of influence available. However, it goes a bit further, and some tools were developped to enforce that rule of peace and order:
-First obvious one, the Church. Cannot influence soul without a continent-wide moral authority known and accepted by the overwhelming majority of the people. And one she is binding to her will in some mystical manner with that blood and Crest Stone sharing. Yes, I'm going there. Silver Snow's finale shows that some sort of bond exists between Rhea and those who undertook that ritual. The fact she isn't using it in Crimson Flower hints that it si likely ont a conscious thing since she is not using it here, but given what happened during SIlver Snow and what sort of things Crest Stones can do, something has to happen here.
-And for when that power fails, you want a military force to purge dissenting elements. Preferably your own one rather than one owed from other actors who may have a stake in what you are purging. Enter the Knights of Seiros. Bonus point, you can have them put at disposal of others while not on a mission you asked them for, so they can go everywhere without question, and are known for that, while building up some nice political capital by being known to do such things.
-Garreg March. It was built a century after? Welp, look at cathedrals in medieval times, they take decades at best, often more than a century, and the size of the whole complex. And frankly, the whole idea behind the monastery is just too important to have been ignored. You want to influence the ruling class and the best and brightest elements of a continent? Be the one giving them their education, so you are the one instillating the values you want to see enforced ('foolishly raise their blades against the Church', people?), and at the same time, by seeing how they behave, you can get a nice measure of Fodlan's current mindest so you can shape it better. And of course, it also means a center of knowledge, a holy siege doubling as an academy for a whole continent. Imagine the sheer concentration of knowledge, and the appeal to erudits, savants... Real good tool for my next points too. Also, it is easier to do politics when your central siege is independant from other powers.
Thing is, that model is all nice and dandy, but there is little problems still: the Elites. Half the continent's nobility was Nemesis' cronies, and they were the majority of the ones with Crests. With time, it would lead to... Well, just see what happened to Maurice's family until Marianne, as was said. So it means rewriting history and the creed to make them heroes too, and the Crests they are tied too aren't dragged in the mud. Okay, needs of the civil peace and all that jazz. But it is the first step on a rather thorny path, one that Rhea now needs to go through to enforce her objectives: Thought control, and its 'needs'.
'But, Cyril! Jeralt! Shamir!' Everyone says at that point. So, elaboration time it is then, from them, to the entire situation:
1) They are individuals. More than that they are individuals directly serving Rhea. No point in squashing them. And even if they were not... Rhea is an ageless Dragon, and I want to give her some credit, please. Destroying everyone not sucking up to the Church would be as impossible as bloody, and ultimately weaken her rule. Fight the battles you can win.
2) However, she also has to get rid of this sort of people the moment they form into groups competiting with the Church one way or another. Look at the catholic's faith history, and how it handled sects with diverging beliefs, and the result when these parallels beliefs became strong enough to be their own faiths (Reformation, and all the wars that followed, ring a bell?). Ideally, you wanted, and want here in the game, conversion or a similar result, but when words failed, it became violence time (Cathars, wars of religions, etc...). And, welp, a faith cannot be the supreme moral authority shaping a continent if it leaves competition rise up, and form into entities contesting their vision of things. Hell, Seteth's solo ending is all about him recreating a more tolerant Church. For this to happen, the former incarnation of the Church has to have been intolerant.
3) And that intolerance leads me to the next point: thought control, not just about deviant faiths, but about history and technology. Because it is the thing with this sort of line of thought. First step is always the hardest, and once committed, retracting is hard. If the Church is caught lying on that one, its core mythos, and there goes its credibility, and Fodlan collapses hard. And the more the scalpel is used to keep that lie going, the easier it becomes to think about using it for other pesky things threatening Fodlan's order and peace, like deviant faiths and how they were crushed, little mistakes at a time or another that were ultimately repaired, the future last point of that list that Agarthans are... People, meet the Fodlan!Index, that list of forbidden books by the Catholic Church. And well, the scholars producing all that forbidden lore have to be dealt with too. Subornation, bribery, blackmail, discredit... eventually elimination if everything else fail. Because censoring history for a thousand years has its cost somewhere down the line, and if you think such process over the centuries is a bloodless affair, PM me, for you have the winner mindest required for succeeding in the business of Bridges Commerce. I've got a nice one in Narnia to get you started. (I guess it also makes me suspiscious of these six centuries of 'peace', or blank in Fodlan's timeline. Normally, RPG like that in medieval times get a pass, but welp, here the game shows some history rewriting is enforced. So big stretches of time with nothing noteworthy become suspicious because foul play already happened. I mean, it's a continent, can you imagine a continent with 'nothing to report' over the course of six centuries of history with medieval societies?)
And of course, it involves technology too. Church have historically opposed research hurting their creed (Gallileo, people), and welp, Agarthans' wonderful example just comes to mind, so the objective here is nipping in the bud developments which could lead to that sort of tech, but also securing samples it for personal use in case of dire need (like Agarthans, but it is not an exclusivity), like the Golems the Church possess and is told in unit descriptions to be able to build and modify. Thing is, nobody else but the Agarthans can do that, so that techno-magical knowledge has to be controled and supressed, and once again there is that 'first step is the hardest' thing, and the fact there is only so many ways of stopping scholars of doing the things you don't want them too, although controlling the biggest center of learning of the continent helps to attract them so you have less need for the bloodier options. After all, someone needs to build these Golems, as I said. (Again, Medieval Stasis wouldn't be something I raise eyebrows at usually, but here, it is enforced. And enforcing this sort of thought control in medieval times... Again, it cannot be done without blood.)
And that comment about Seteth in the library in GD also shows that such thing is still being enforced. So nah, regarding to above posts, I have serious doubts that pre-war Hanneman, as in 'when the Church is enforcing the thing I mentioned here', would have been able to go for much longer. And post-war, these politics are done, for a reason or another.
4) And there is another reason, the big one, for all of that: Agarthans. Rhea knows these duckers still exist, becuase welp, they survived Mama's wrath to help Nemesis. She knows that GD, and would have to be brain-dead to not to: how would have that two-bit thug succeeded with the whole Crests and Relics shit like that otherwise? And I can bet he had some Agarthans soldiers inside his armies, and the corpse-like weirdos are hard to miss, and failing all of that, there were the Elites to question after their reddition, and again, I'm giving Rhea some credit here. And in the name of that credit, I will go out on a limb and assume she knew better than assume the Agarthans were all dead and done after that. Hell, her own Mommy Issues would forbid that too, both because she needs them dead to finish her vengeance, and because she is firmly in a mindset of 'only Mother knows better', so she won't dare assume she succeeded in killing them off when Mama clearly 'failed' until Shambhalla is found and reduced to a smoking crater. And again, it doesn't take a genius to assume they will try again to burn Fodlan to the ground and kill her and her remaining fellow Children of the Goddess. Henceforth, she needs to fight them and root them out, and that means shadow war. It means be on the lookout for Agarthan infiltration, for signs of their tech, for 'poisonous knowledge' they could spread to further their goals, which pretty much sends back to the points I mentioned above, except this time the goal is fighting off Agarthan influence. With the Knights to purge the enemies. And since the other facet of that mindest I mentioned above is the underlying opinion that she knows better than everyone but Mama for the whole continent's sake, it is why she is doing that shadow ruling people, it means keep the direct knowledge about these guys to herself, both to avoid them damaging the picture and society she created, and to avoid people wanting to contact them for a reason or another to get their pretty much poisoned 'help'.
So, these are the basic staples of Rhea's rules, and the reasons for doing shadier things, because if nothing on these fronts is done, her whole power eventually crumbles like wet paper and she loses any mean of enforcing that peace and order she wants to.
Thing is, her rule when the game begins is already failing.
The Crest/nobility problem? I see it as nobles seeing the emperor getting that 'divine sanction' from Rhea with each new crowning, and deciding they wanted a 'divine right to rule' too. And well, they had Crests, tangible sign of the Goddess' favor, and the illustrious pedigree of descendants of the sacred 10 Elites, it has to count for something, right? What's that about abusing Crests? but, their ancestors fought Nemesis, clear sign of being Goddess-approved, and the Church isn't condemning them, as it would if that was something improper. Lesser nobles probably used the excuse of 'I work for the guy with Crests' as their own close equivalent to that maneuver.
And Rhea did nothing when that idea cropped up. The reasons can be multiple, liking to see Crests, these last memories of her people, being given proper reverence, indifference to that shit, inability to see how it would eventually develop, deciding the conflict to ban that line of thought wasn't worth it... But it was still nothing, and it planted that 'divine right to rule thourgh Crests' idea. And it keeps going down to shit from there. Because Crests really become a sign of divine favors for these future generations, so they need to manifest, at all cost. Minor were surely scorned at first, as a sign of weakining divine favor, but as they faded, Fodlan's nobility discovered it was literally losing what they had framed as their right to rule, and without it... Welp, they would look like fine and dandy once deprived of it, so it led to more and more... discutable measures to keep this going. And Rhea did nothing as the situation slowly rotted, when she had that termometer that was Garreg March, despite the fact the ruling elite's slow programmed death was very much her problem, because once they collapse, no more peace and order, and the Church who helped them so far, if only by inaction, will have to give answers. And yes, she is accountable for that. She claimed responsibility for ruling all of Fodlan, so what happens here falls on her head. You rule, the problems cropping up, and how they are dealt with, become your problems.
And of course, tell a social class that they have a divine right to rule for a few centuries, and it breeds some serious entitlement into them, leading to the corrupt ducktards causing so many problems in-game. And again, no correction attempted before it is clearly far too late for the problem to be removed cleanly. And Rhea is an ageless dragon, she should have seen this slow evolution with her own eyes, recognize the trouble, and settle that. She didn't, and voila, here are the results.
And there is also the slightly total failure about that shadow war with the Agarthans, when you see they can infiltrate Garreg March, stir up shit like the Rebellion of the Seven and the Tragedy of Duscur to keep rocking the boat until continental war happens while making sure attempts to remedy to the ambient shit are destroyed.
Hell, it reached the point where she is losing control of her own tool of ruling, the Church. See the duck which has been going for years with the Western Church. Assassination attempts, then open war when what purges she attempted failed. Yes I said there were such things. It has been years of conflict by the time the game happens, complete inaction of her part would have been a demonstration of incompetence so blatant she couldn't have lasted a thousand years. And the last assassin caught in Chap.4 bitches and moans about how so many of their brethrens have already beeen killed so far. Likely more than the strike team, and these dudes don't strike me like the sort which would think much of pawns like Lonato and his son, so it has to be them. Likeliest reason was enquiries andpurges about Agarhtans infiltration when this whole doctrinal divergence cropped up, festering until war.
Hell again, the Empire's fracturing is part of that misrule in some way, if only because the wars which happened here are parts of the sort of things she wanted to save Fodlan from. It means some serious misformation of the Empire's nobility while they were at Garreg March to lead to a situation where independance was a desired outcome for the local pouplations, and a failure to find a decent war-less solution. The negotiations she did here were a good thing without doubts (and helped get some political capital for later), but at the end of the day, it is damage control. Fodlan is canging to much for her model to keep going, and the strain is now showing.
Worst part? Rhea is intellectually aware of that to some degree. That's part of her reasons to resurrect Mama. Mama knows better, she'll know how to fix it all. Except as failures after failures pass, she devotes more time to this rather than searching for actual successors, and the situation keeps rotting. And since only Mama knows better, it also means crushing dissenters, without questions.
And so the pressure build up unitl something like Edelgard happens, once the system rotted so much it collapses.
Given the fact this is medieval times, with only one dominant faith, I find it telling that Adrestia isn't rocked by pro-Church uprisings during that war. Look at conflicts between popes and emperors, people. By all right, Edelgard's rule should be contested widely, with several revolts, guerillas and the likes inside. Agarthans can help with the nobility (to a point), but not with the populace's anger, whenthey are not stroking it (see Ferdinand/Lysithea's paralogue). And what happens? One mention in the first chapter of post-timeskip Crimson Flower only, no Resistance known, no mention of bloody repressions... looks like the opposition (she attacked, and maybe, captured the pope! No way it is 100% approved by the people, including the believeing people who will be a part of the army too. That's called desertion) isn't really strong. The one uprising is that paralogue, and it is all because Tharundel is rocking the boat for the after war. And I'm fairly sure it doesn't even happen in Crimson Flower, when the Paralogue doesn't happen, for several reasons:
1) More moral Edelgard means less given to the Agarthans. Which would mean not giving the place to Tharundel.
2) Since Aegir was spotted there? You bet your skinny ass Edelgard is going for the one figure which could lead an Imperial opposition, especially if it allows her to enact some vengeance without turning him into a martyr for the opposition.
3) Uprising means lost resources, insecurity, lost troops... Why would she let it fester exactly?
And I want to bring to attention Revolution in France. When the axe was really taken to the social order, the pope condemned. He only had a shadow of the power of medieval times, but the conflict was enough to spring many uprisings, including a guerilla which lasted for years, despite some truly heinous methods used to crush it. The only way Edelgard escaped even that is if the Church's power is truly in tatters, and its crediblity iredeemably damaged. And that hints to a pretty epic failure in rulership.
And as a PS, I'll point out to the Verdant Wind route, after Rhea is freed: First answer when confronted and asked for answers? Bullshiting, aka only Mother knows better. Claude has to use a bloody pair of pincers to pull the bloody answers out of her mouth, and she only truly fess up after the ultimate humble pie Shambhalla is. That unwillingness to share knowledge even once the failure is patent, to cling to her way of doing things against nearly everything... That sort of little things just stress how uncompromising Rhea actually is. This is the sort of everyday behavior hinting at bigger things that tells me that barring that whole war, nothing more would have changed than compared to the last thousand years of zero changes.
It would be also why the Azure Moon ending is the one I am the most dubious about regarding Fodlan's future. By itself, a system reboot fixing that corruption with new additions, and likely nothing of Rhea's measures for the good reason she isn't in power anymore are good things. But just like Dimitri told Edelgard was mistaking disease and symptoms, the disease is still there for next time: Agarthans, still existing as a group to try again someday, and a Rhea which hasn't fully processed the humble pie. So once Byleth goes away, I expect her 'Only Mama knows better than me' line of thought to push her to make a move for her old tool the Chruch (or any new more adpated one) to try and keep Mama's peace going the best she can... And she arleady failed dramatically on that front once.