He is bound to be a bit stressed after a cage move. I would give him at least 6" of bedding - more if possible
He'll soon be digging and burrowing. Also after adding the new things, maybe give him chance to adjust for a few days before taking him out. But if he looks desperate to come out and continues to chew at a corner, then maybe let him have a bit of out of cage time anyway.
Does he have a house that's dark inside? One thing that can make them feel stressed and wanting to escape, is if there is no dark place to nest. That would either be deep bedding they can burrow down in, or a house that's dark inside. A shoebox house is fine and if you put a bendy bridge over the door it makes it dark inside (light doesn't go round corners).