Congratulations on your new bunny!
I would say he is litter trained but what you are seeing now is him marking new territory. As scattering of poops as he hops around the place. You’ll be happy to know this is normally short lived.
I don’t know if you’ve has rabbits before, but their poop really doesn’t smell. But when they do territorial droppings, those can smell. Have you noticed a funky smell at all? There is a slight sheen on them and its that coating that produces the smell. (This is different to the ultra glossy cecatrope droppings that they reingest).
Some things that might help is limiting how many areas his allowed access too, only allowing smaller areas at a time. Then increasing space over time. Also, popping some extra litter boxes around would encourage him to use those hopefully. I really do think this will naturally abate though. It may take a week or two.
Have you found yourself a vet with rabbit experience as yet? It’s a good idea to know your options so you’re not caught out when a pet falls ill. Maybe get him in for a wellness check and the vet can let you know if he has definitely been neutered or not. At 3yrs old, you should be able to see the testicles but rabbits can trick us by pulling them back up into the abdomen. 