I would probably just try to snare whatever it is, personally.

Beaver don't tend to return to a tree. If they get spooked off it, they go start on another later..

Looks like that beaver is long gone I’d be moving on from damage that old and not even recognize able you might be chasing a ghost.

Not beaver damage. Ive seen that here in places where there are horss, goats or sheep.

Another vote for porcupines.