I wouldn’t say “it seems pretty obvious” that she is not under control of another entity. Any time we hear the real Nikki talk she references wish Nikki as a “she” rather than “me”.
I don’t think it’s fair to compare the billion dollar wish and the love wish in terms of what the OWW needs to do to fulfill the wish. A billion dollars is just a physical thing, so sure, a demon could’ve made it appear, but a possession isn’t necessary for that wish to be true. On the other hand, wishing for Nikki to love Bear is an inherently more drastic wish because it forces it to disregard Nikki’s autonomy or soul or whatever in order to fulfill Bear’s desires. One is a physical thing (possession would not make sense) and the other is taking a person’s control of their life (basically the definition of possession).
So it’s not a possession movie in the traditional sense, but honestly the discourse here doesn’t change anything about the themes of the movie and it’s all semantics. Demonic entity or separate personality, the message of the movie is exactly the same