Yip the biting is out of fear, not out of boredom or aggression or anything like that. Most “bad” things rabbits do are caused by fear, so try to see things from that perspective.
Try not to put your hand in his cage or move it towards him quickly as this will startle him. He’s in a new place and bunnies take a while to relax and settle in, so he will be on edge and scared for a wee bit. Lie on the ground and let him approach you, don’t move but do talk softly to him. You can try to lie a treat on you or your hand, just as long as it’s always him approaching you. One of my bunnies was like yours when we got him, and it took us a long time of doing this to get enough trust for him to even let us move a hand near him safely, then touch him, then pet him. Now he is a little beggar for nose rubs!
Only clean his cage when he is out (and don’t pick him up to move him out of it, let him hop out himself). Rabbits are very protective of their space and belongings, and right now when he is in a new place he is going to me more scared so more defensive. If he does bite you then let out a high pitched squeal to show pain.
Definitely try and get him a stuffed toy companion. One of my bunnies loves to groom his toy bunny, and also the furniture and blankets! Make sure it is safe for kids/pets though (we got a realistic rabbit soft toy for dogs). This will help him settle in and give him some comfort.
Good luck with wee Henry, I’m sure all it will take is time for him to feel relaxed in his new home and his behavior will improve!