That was a larger animal, a rat will not spread damage over that large an area. Where you are you can have bobcat, fox, coyote, dog, possum, skunk, and raccoons to mention a few. That could have been any of them.
If I remember right from your other thread that door only opens out and you have a stop behind that door to keep the critter from pushing it in. The critter tried and quickly gave up.
Two ways to identify the critter are footprints or scat (poop). I know it's been a bit but if you could find some poop and take a photo we might be able to help identify it. By now you are not going to find identifiable paw prints but you can prepare for the next time if it comes back. Raking the ground smooth under the door may be enough, but if you scatter some flour that can really help. Maybe even put a flat board down there with a dusting of flour. At least you'd now what you are dealing with if it comes back.