I just re-watched TNG “In Theory” (S04E25) and Data says that the door to his quarters is set to only allow humanoids to enter or leave when Geordie finds Spot in the hall.
Whilst I get that it would be dangerous for Spot to wander the ship freely I think it’s kind of mean to keep him locked in a small room like that forever. There doesn’t seem to be any cat toys in the room but maybe the computer is capable of some sort of environmental enrichment we can’t immediately see.
Yeah, I get the impression TNG quarters are about the size of a studio apartment, which isn’t amazing for cats, but it can work if you keep them entertained.