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.
They used to be allowed to run through the decks but then they started peeing in the Jeffrey’s tubes and engineers couldn’t work with the smell.