I expect he couldn’t control his poops both during the messy ones and with the ones afterward. He just may have felt better, and let loose where he was. He has been ill, and unless he is really fine this weekend, I would watch carefully for a new incident of poopy butt and if he does that again, call your vet.
Yes, there is a bit of cleaning that needs to be done to help him feel better. A clean litter pan will help. Also, wherever he made a mess on carpet or outside the litter box, you can clean it with a solution of 50/50 white vinegar and water. That will get the smell out so he stops being attracted to those spots.
As for his butt leaving traces of poo, just get a soft cloth and dampen it a little, then gently wipe his butt and feet. It should take off the excess and he will want to clean himself after you, which will also make him feel better. Bunnies don’t like to be dirty, but shouldn’t be given full baths either. They clean themselves, but sometimes can use a little help.
Hope he feels better soon!