For the males, you sometimes actually have to keep them from running around as they are usually ready to run about before females. So you may want to get him some boredome busters l(check out the homemade toytest section) example: stuff hay and goodies in a cardboard roll. That way he can keep busy without running around. (They can actually pull out their stitches if they are jumping up and down on furniture too early after surgery) The stitches will dissolve – or at least that is how they are mostly done here.
Great that you have soft stuff for him to lounge on. Just make sure he is eating and drinking, and that the incision is healing properly.
Regarding having to wait to adopt your other bunny – honestly, unless i misunderstood the post, I can understand why the place/person would want you to wait if you have all this stuff going on in your household as it’s best to have a peaceful quiet place where he can settle in. It’s actually stressful for a bunny to be in a new place in the first place (even though it may better!), so I just imagine she was looking out for the bunnies best intereset and wants to make sure the transition is as positive and nuturing as it can possibly be.
I’m excited for you though, so keep us updated!