I wrote an old version of this post long ago (like two years ago), but now I want to write it better. So here's an improved, longer version of this note:
At the end of Crimson Flower, Edelgard successfully kills Rhea/Seiros, and then she unites the continent of Fodlan under her rule. The Adrestian Empire rules over all it surveys. Rhea, Dimitri and all the others who stood in Edelgard's way lay dead and buried. But (since this is something you can do in Crimson Flower), a few people got away. Byleth had a weak heart, and Claude, Seteth and Flayn all escaped Edelgard's wrath. Presumably, they fled Fodlan for parts unknown. Either that, or they went into hiding, to await a day when they could have freedom.
Since Edelgard had already dealt with Rhea/Seiros, I can't imagine she'd even bother knowing where to look for the other relatives of Seiros. She seemed busy destroying the church and the crest caste system to care about a bunch of legendary dragons. So we can also assume Saint Indech and Saint Macuil survived and probably went into hiding alongside their kin. That's an assumption I can't prove, however.
Now… I don't need to go into what happened to every character. Because you can make logical assumptions, all based around their ending credit lines and stuff. So we know that Edelgard destroyed the Church. We can assume she got rid of crests. We can even assume she went after the agarthans after dealing with Rhea, successfully driving Thales and his kin even further into hiding (where they might be forced to make a truce with the others in hiding, like Seteth and Flayn). So depending on your view of things, Edelgard achieved a lot of good (or at least a lot of her core objectives). But she did it through extremism. And so nothing is truly stable.
Cut to 100 or 200 years after Edelgard's death. It's now the reign of one of her great grandchildren or descendants, and things aren't going very well. State Athetism has become the lay of the land. Her successors took her lessons and only radicalized them further. If you have a crest and refuse to get it removed, you're shunned from society. If you have any sort of ancestral connection to the nabateans or the agarthans, you're exiled from society. Hells, there's even prejudice against people from Brigid. And it's an empire vassal state! The old caste system of nobles vs commoners has been replaced by a new racial system. Things have stayed the same, only the circumstances have changed.
Into this world would step our protagonist, a newcomer to fodlan who hails from a distant continent. Coming to this land to visit their family, they find their cousins have all been exiled to the slums for their lack of proof as to their heritage. Trying to stand up for their cousins only makes a protagonist a target, and thus they step into a world of racial hatred and mad extremism. In the end, they'd be dragged into becoming the leader of a resistance movement dedicated to liberating the peoples who've been abandoned. The agarthans, nabateans, brigideans, etc.
I feel like the resistance movement might be tied to the old underground sanctuary of abyss, underneath garreg mach. Abyss itself is gone now. But New Abyss exists. An amazing labyrinthine kingdom hidden underneath the empire. A sanctuary for all those who the surface dwellers view as lesser or inferior. A safe place for people to be themselves, to experience faith and religion, to embrace cultures not of adrestian origin, to be different and unique.
Very few characters (beyond Flayn and Seteth and maybe the other nabateans) from the original game show up physically in this story. But their descendants show up. And statues and portraits of Edelgard and Hubert and Byleth and stuff would be likely seem everywhere in empire territory. The extremism has intensified in the centuries since, but the new emperors all claim they're doing as their great ancestor would have had them do. Proof that good intentions with bad means will always lead to bad results in the long term.
