Remember this isn't a 'possession' story, where the Isekai'ed MC wakes up in a character's body, it's a reincarnation. Ren grew up from birth in this world. She just didn't remember her previous life until she nearly died in the carriage accident.
Most of the time, it doesn't matter which it is. Nor that it's even an isekai in the first place. I think about 70%-80% of isekai stories can be rewritten to be more like DanMachi, which has the exact same feel as most isekais without actually being one. In 90% of where it does matter it's just that the MC knows exactly how to construct modern technology only invented in the last few thousand years, like water pumps, crop rotation, or soap.
And in a lot of cases for this specific variant, there's little difference between an actual possession and a reincarnation with memories of the previous life. Sometimes the character herself doesn't even know which it is. The old memories suddenly appear, and the character doesn't know if she just got placed into a body with access to the body's memories, or just remembered stuff.
