and will most likely chase him away from their turf and their regular food supply (you).

I hope he's chipped, that's the best hope s/he has of getting the kitty back again.

Cats are really attached to their home territory, so poor Thunder might be trying to go back to their old place, even if it's hundreds of miles away.

She was a spayed female but still worried she'd run off and get lost from the new place. I kept her solely indoors for the first few days but her demands to go outside became insufferable. Everything was fine. She hung around the immediate area when outdoors. But she didn't have a bunch of other cats around like the OP. Thunder might leave and come back in a year. Cats are interesting.

I always gave my cats a couple of weeks. I wanted to be sure.

I might have let the World's Dumbest Tomcat (TM) out, but only after a few days of cleaning up his messes when he'd get into the litter box, hang his arse over the edge, and do his business on the floor. Yeah, I used newspapers, but jeez. At least he wasn't too stupid to ask to go out when he needed to go.

I am still checking around, though.