You should probably confine him in some way but it also isn’t good to stress him either. Could you add a small playpen to his cage so he can still come out but can’t run laps or anything? After his neuter, keep him warm and quiet. You will want to make sure he is eating, although this usually isn’t a problem with boys.
Rabbits are not able to vomit, so you should feed him normally right up until his surgery. Is your vet rabbit-savvy?

You should feed him his normal food before surger, and not just the night before. Of course it’s good if that’s hay, but the most important thing is that he does NOT fast. Rabbits’ tummies must never be empty or the gut may slow down to a stop, and that is extremely dangerous for them.

After the neuter, eating and pooping is the most important. Keep him warm i e see to it that he doesn’t get cold. You’ll be able to see a lot from his behaviour. Excess attention to the incision area may signify pain. Sluggishness may be due to pain or low body temp. Restriction/confinement is so you can keep an eye on him, if he f ex hides under a big bed he can pull at his stitches or start to become sluggish without you noticing-, or he could be binkying like a mad bunny in another room and you’d not be there to stop him. If you have a good eye on him he doesn’t absolutely has to be shut in in a cage or so.

Water is best served in an open bowl, a bottle may be too much work.

Best of luck! Boys generally do very well after their “procedures”.