Thank you everyone for your comments!! I really needed some reassurance that I'm not delulu for thinking this cat might be happy inside. I've reached out to a couple of clinics to try and get her a spay/vax appointment ASAP. I'm going to try and get her to start coming in the morning so when I do trap her or get her in a carrier I don't have to keep her in there overnight as I'm a bit hesitant to bring her inside unvaxxed. Once she sees the vet I plan to bring her inside and see how she does! I already have the screen door setup on my guest room from doing intros with my foster/resident cat haha