THIS! Like it was her own dumb logic going "he started the war --> I died bc of the war --> he killed me" which isn't true, a part of me thinks she said that for a comedic element in the story (idk at least for me that didn't read as serious at all, she doesn't seem to hold any specific resentment or fear towards him that she would if he really did kill her, rather than just general caution around him). Ofc it could be that there was something more to it but it really doesn't seem like she died by his hands, or if there was, I feel like it would be a desperate situation where he had no choice (with the way he is still longing for her 6 months after her death, and considering they didn't seem to be that close from her view... bro had definitely fallen before he even realised it).
Y'all the crown prince is the reason of the WAR, but that DOESN'T mean he is the reason why the FL died. She probably die because of some unknown soldier or because she is already weak due to the GEM getting destroyed in her heart.