I have not managed to capture a city state yet for fear of what would happen. Do captured City States get Occupied forever preventing growth? Or do they not get Occupied Status? Pro Con of capturing city state because it would make no sense to me if you get stuck with occupied status.
If you capture a city state in Civilization 6 it will give you 2 options:
Capture or Raze
You can raze city states forever. If you choose to capture them they will not be occupied and will behave as a normal city.
Liberation is a third option if you are recapturing a city state from another player.
NOTE: City state special bonuses are VERY powerful in Civ-6 and these disappear when you take over or raze a city state (in case of razing that special bonus is gone forever).