I haven't even found a cat are they even on the island

According to the Wiki these naturally decay into pelt, so if you have a couple of cats and pet them, you can get a tiny pelt stash. Not good for mass grinding, but can be helpful if you've just finished a pelt run and are still off by like five or ten, if you're willing to wait 2 minutes

Can confirm they are on the island but im guessing super extra really rare bc I’ve played well over 100hrs and have come across literally one. Their name is Beans.