I was thinking what if her past memories bled through but not directly or fully remembered until the coup?
Like being drawn to Lazlo whenever he visits Obel. And being the first person other than her dad or Ferid she trusts without a hesitation. He knows who she is because past her was his friend, they fought the Kooluk together and helped form the Federation. He knows of Catalyst Rune and what Kar can do-- in fact before her fateful encounter with Yuber she trusted her journal and some other things with him knowing she was likely to regenerate. And if the ship carrying her guardians wasn't wrecked in the storm, it's possible Lazlo would have raised her on his island away from the eyes of Harmonia and others as per his request to Leknaat.
(While well intentioned he may have been, I think it was better for her to have been raised with the Egans on Obel. That socialization with her siblings was important for her development, after all.)
If I bring back her stealing the gun from the Howling Voice Guild when Ferid basically jailbreaks her From Harmonia...it's because it's her gun. In a past life she co-founded the Guild, and that was her gun, and that's why current Kar seems to be drawn and knows how to use it. (As well the knowledge of black powder-- she never stole that from the Guild she just knows and it disturbs her and frustrates her because she's (understandably) not believed.
Or remembering some part of the Grasslands or Scarlet Moon when she'd spent little time in either as the Harmonian envoy wanted to get her to the Crystal Valley as soon as possible. How she felt drawn and how familiar Leknaat seemed when she summoned Kar to her island and basically told her she must return to Falena for things to play out.(Ending the "summer fling" with Georg and setting into motion a whole bunch of shit.)
(Sidebar: they never mentioned how old Leknaat or Windy were, but given how much Leknaat is linked to all the games/the fates of the 108 stars/the True Runes... I've no doubt Leknaat has seen/protected Kar for at least 2-3 regenerations.)
And once in Falena, how comfortable she is navigating the Feitas once in Falena. Like she's a natural born Falenan and not a newcomer. Olhazeta is one of the few that believes her because while Kar is a little gremlin who makes shit up for fun, this isn't a joke to her (Ferid too, because he grew up with her and has seen this strange behavior since their childhood. It does hurt him to know his sister doesn't have the answers but will help in any way he can so she can have them). In fact it disturbs her much more than she lets on. She cannot explain why and even the wisest Rune Sages in Harmonia wouldn't tell her. (They were ordered not to by Hikusaak mind you...) While she can't remember (yet), in the past she once served another queen many many years ago as a Nether Gate agent.
And even in that incarnation had a similar situation because a previous life before that one lived in this land when it was still part of Armes as the last king's consort and bore witness to the Sun Rune's power then. She'd killed the man she loved to stop it but it had been too late. The land was scorched, and it was only when the Sindar arrived that the continent was the land restored with the Dawn and Twilight Runes. And following that the foundation of the Queendom of Falena as we know it.
Kar probably goes a little mad after Ceras, both with trying to reconcile at least 1000 years of lives and finally things making sense and feeling vindicated for being not taken seriously or believed. Mix that with her grief and conflicted feelings about this war it was probably unsurprising she had her little breakdown to get it all out and regulate herself again. Jeane was definitely a huge help, Zerase was not, but at least divulged some little information to help Kar reconcile her past lives.
