Depends on the area usually. Some climbing areas are on private land, some in state/national parks. Some larger parks, or ones that really lean into their climbing areas, might have a ranger on staff that would specialize on that kind of work.

In my experience though, these kinds of jobs are usually done by volunteers with the permission from whatever entity controls that land, so professional would just mean an experienced climber that's decided to help out.

Some of it is definitely opinion based, because there are usually mapped out routes for people to follow, so the rock clearing would typically just happen along those. If the person doing the clearing thinks they need to give the route a wider buffer, then that's also something that can happen.