this seems like it might be different from the LN, iirc in it
the heroine ends up betraying the mc at the demon king's castle (who by the way was apparently just another person who had black hair and powerful magic i think?) and nearly killed her if it werent for the revive necklace patrick convinces her to wear, then the heroine ends up getting killed
in general i think there was a lot more animosity between the prince/heroine and the mc, but tbh i by far prefer the "become friends" trope to the "heroine is actually the villainess" trope