Hi there! Clover sounds like a very sweet bunny! I have had the same experience with my bunny that you had with Clover! Pepper would always hold on to the side door of his cage and shake it with his teeth. I found out that meant he wanted to run. Pepper also did it at night when I was sleeping, and would wake everyone up. NOT COOL But I found it helpful if I put a bath towel ( bigger than a hand towel ) over his cage ( covering the side door which he shook ) when I went to bed. I guess he sorta got used to it and now he knows that when the towel is on his cage, it is time to sleep/ be quiet.

I hope this helps;if not I’m sorry, i’m a first time bunny owner.

The first thing that comes to mind is that maybe he feels safer under the bed. Does he have somewhere in his enclosure where he can hide in darkness and be comfortable?
As for the bar rattling, not only it’s loud and annoying but he might hurt his teeth if he does it compulsively. You can secure the bars by shielding them with cardboard, so that if he’s chewing he’ll chew that and not the bars

Yep, cardboard facing inside It will give him something safe to chew (they can go through cardboard pretty fast so make sure to have spare pieces) and maybe if the view of the underbed wonderland is blocked he might feel less franctic about it. You can use plastic zip ties to secure the cardboard to the bars, so even if he tries to chew them he won’t get hurt

My bunny used to do this all the time. I ended up threading cardboard through the bottom of the pen and he stopped! I.t also helps to put toys in front of the area that he likes to push and pull the pen