It finally worked. I don’t know if it’s a new update or what but previously I didn’t have two factor authentication enabled. I enabled it and now it worked.
(I don’t know if this is relevant but I logged out of my Apple ID on my “Mac" and logged in again but I never logged out on my iPhone)
I have no idea if this is relevant or they just fixed it somehow but I thought I should share it.
My solution was to clear the Play Store cache and storage, force stop it, and restart. Then, clear ChatGPT’s cache and storage, force stop it, and uninstall. After reinstalling, it worked again.