To my understanding it Seems like it the original FL let the reincarnator take over because she always wanted someone to need her and that was the reincarnation ...but she wanted to be away from society and the only way to this was helping the villainess
I'm pretty sure it was two souls. With the reincarnator having main control over the body for all the years that the "game" was occuring. And the original only being able to use the body while she was asleep and at the very end when the reincarnator was locked up in the mind
so did she just had a split personality or were they two different souls?like one being the soul of the reincarnator and other is the original fl?