The allergy issue is something you need to check up on. It might vary cat to cat, and possibly be mild enough to not require heavy medication. Otherwise, it might be that the allergy reaction constantly affects your interactions and relationship with the cat.

Beyond that bringing in new cats is a on-going process. (I have two new adoptees if have been in the apartment less than three weeks.) They take time to get used to a new environment, a new routines, and new staff. “Enough is enough” is a good way to describe it - give them a “safe haven” and they will start interacting with you and establish a social rapport as their comfort level grows.

And make sure the cat gets social time when it wants it, and things to interact with otherwise (window sills, toys, etc.) Playing with them is interaction time as well. And they are good at telling you when they want to quit.

At this point with my adoptees the younger cat comes and hangs out with me a lot. The older one (who the shelter described as a bit of a trouble cat) comes around for pets now and then, hangs out in the room, but doesn’t do laps or climb up on the couch to get pets (yet).