Hey there anon! Thanks for the good vibes 😀 right back atcha.
As someone with at least one immortal kintype I’ve examined this question a lot personally.
Here are the possibilities I personally ascribe to reincarnation theory with immortals: (the ‘you’ here is a nonspecific you referring to any immortal in question)
*something at some point was stronger than you and killed you, or you somehow for some reason ended your own life.
*you existed to the very end of that universe, and when that universe ended you stepped into this one, or another.
*The universe is still extant, and you are still alive and you are projecting your consciousness in some way across universes into this existence (and may return to your previous immortal existence at some later date).
The third one is the one I think was ascribed to most back in The Day by various immortal kin, but I have only anecdotal evidence to back that up.