So there’s actually a detail about Catherine’s backstory that looks a bit weird if you take it at face value: in her A support with Byleth, Catherine says she was falsely accused of participating in the regicide so she had to leave the Kingdom, but the really important question here is who accused her and why, and how did it stick to the point she had to run away
Because Catherine clearly isn’t on bad terms with Dimitri or other eastern nobles, they don’t act like they believe she was involved in killing Lambert so it probably wasn’t an eastern house that accused her, and even if she was accused it might seem odd she had to outright leave considering Charon is geographically and probably politically surrounded by royalist houses
But the thing is that she did not lay low post-Tragedy, she turned Christophe aka a western lord’s son in for execution, right after a successful conspiracy + decapitation strike on the king the general western Kingdom elite cohort was involved in; and we know it wasn’t an anonymous tip-off type of thing bc Lonato knows she did that and has an axe to grind against her
So I think in the aftermath of the Tragedy the Kingdom was implicitly or explicitly having an east vs west struggle, and while Western Church was trying to take advantage of the chaos to off Rhea in implicit or explicit coordination with the western lords, Cassandra interferes
Western faction probably got pissed about having their kill steak interrupted and accused Cassandra of participating in the regicide to get back at her, everyone including western faction probably knows this is bullshit but this is a shitslinging power struggle where they’ve already decided on the conclusion and are working backwards
And most crucially Rufus the regent and Cornelia (Cleobulus) as court mage were both allied with western lords and involved in the Tragedy, so if they supported the western lords’ claim that Cassandra was involved and pushed that as the official narrative, others probably couldn’t do shit about it
So Cassandra now has a target on her back, and if other eastern houses including her birth family attempt to protect her the western lords have a pretense to accuse them of sheltering a treasonous criminal and attack them (literally or politically), if she seeks asylum in Empire or Alliance it has political implications due to being Crested Relic-wielding member of an important Kingdom family
Hence she ran off to Garreg Mach and took on a new identity as Catherine because it’s Fódlan’s neutral ground and they already owe her kinda for reporting the potential assassination plan
Tl;dr Catherine’s extended political context edition backstory might be something like “local noblewoman tries to stop situation from getting worse, gets branded traitor because people doing it are powerful enough to do so, learns that truth does not matter during power struggles the extremely difficult way”
Even more tl;dr would be that Catherine might have turned in Christophe feeling conflicted only for Christophe’s regional peers to be like