Bunnies shouldn’t really be separated from their mums until they’re 8 weeks old, so he/she may just be subdued as they’re still pretty young and have been moved to a strange environment. I wonder if maybe he’s overwhelmed by the space he has too? Even if you have a free range bunny its good to give him an area that is ‘his’ with hay, food, boxes etc that he can always retreat to.
But bunnies aren’t ever really ‘playful’ in the way that a cat or dog would be. Normal bunny behaviour includes some speedy running and jumping, but also a lot of flopping and snoozing.
Have you tried sitting on the floor with him at letting him come over and investigate you?
You might also want to give him more pellets while hes still super young. I’m not sure what a 6 week old bunny should be eating, but babies should have more pellets than adults. Hopefully someone else can advise on pellets, but I gave my 8 week old bunny 2 small handfuls a day. He’s now about 17 weeks and still getting that amount, but I will be slowly reducing over the next couple of months.