I have a theory after watching Obsession:
Something struck me when I saw Obsession a few days ago for the first time. Yesterday, I rewatched it and that reinforced my thoughts on the subject of the cat. Which is that the repeated referencing to the "cat" has a deeper, double meaning. I tried to look at other threads and discussions before posting and don't really see much about my specific thoughts, so hopefully I am not being repetitive. Obviously, I could be way off and/or overthinking the film, but here it goes:
I think Curry Barker was using very effective subliminal messaging from the very beginning to articulate to the viewer that Nikki is no longer truly Nikki when her free will to be with Bear is taken by the wish. That the chosen phrasing used whenever the "cat" is referenced is designed as double entandre.
We know that Bear's cat, Sandy, dies after eating medication, but there are several scenes in the film where the cat gets extra emphasis throughout the plot. When Nikki makes the memorial, when Nikki brings the vase of flowers in the middle of the night after watching Bear sleep, and when Nikki feeds Bear pieces of Sandy in his sandwich. Bear cared for this pet, but I don't think it was meant to just be taken at face value that each moment is referencing the actual animal.
Immediately after Bear makes his wish and Nikki returns to his car, she is clearly different and infatuated with him and trying to have him spend time with her. He is obviously caught off guard with her sudden change of demeanor. Trying to convince him to stay, she says, "Do you want to come inside? I did just lose my cat, Bear." The viewer is also confused and taken off guard by her chosen phrasing. I don't think Curry Barker was just simply writing her words for the sake of making her seem off or weird. I think it was very good writing to illustrate her loss of control in this situation. (What she did just lose moments prior was her personal agency.) Bear is obviously confused because it isn't her animal, and this is where I believe "cat" first emerges as double entandre. We have the literal cat, Sandy, and the figurative cat: Nikki's personal agency.
The name on the back of the One Wish Willow box is called "Tabi Cat Curiosities" and it appears over the hotline that Bear calls later on. Again, I think Curry Barker is using the word "cat" as clever subtext to mean Nikki's presonal agency in this relationship. Another example of this is when they first get the relationship going and they are in bed and she tells Bear she's sorry he lost his cat and he replies, "I think you got me beat there." While on the surface, he was talking about her dad and cancer, I think that was another very subtle line where Curry Barker is telling the viewer that we know and that Bear knows he took her free will away with his wish.
The other main part where this idea struck me was the packed lunch scene where Bear sees the Polaroid of himself that Nikki packed, which says, "You" under Bear's image and the other photo with them together that shows "Not Me" under Nikki. There is a post-it note on his sandwich that says, "My little food critic." Moments later, Sarah reveals that another message is on the back of the post-it: "What's the verdict: Cat?" Taken literally without more thought, the question is obviously about the contents of the sandwich. But perhaps Bear is being asked a more veiled question: what is his verdict on his wish? Is he happy with his control of her? Be careful who you wish for. (At this point in the film it is more and more apparent that he is not happy with how things are going with his wish but he persists anyway with his codependency and desire to control.)
Thinking of it this way makes me think the earlier scene of the cat memorial may also be a symbolic mourning of Nikki's loss of free will and her body. The One Wish Willow box showing the viewer "Tabi Cat Curiosities" above the hotline number was no coincidence in my mind. Borrowing from the old saying "curiosity killed the cat", in Curry Barker's world, curiosity can kill the cat literally and figuratively.