
Theory: The obsession is not Zankou's, but yours
The playable Zankou is just an illusion, and even she knows it. She doesn't even exist physically, so Coco giving her gift is similar to a devotee giving offerings to something they can't see, something they're obsessed with or believe in, similar to a god.
So giving this Zankou gifts, inviting her to home, going on dates while Coco despises her increases Coco's obsession towards her, worsening their mental state.
This is interesting for me because for any other characters, increasing their affection means making them like us more. But in Zankou's case, it's Coco becoming more obsessed and crazy for Zankou the more they give her gifts.