The US Space Force (USSF) is the successor to Air Force Space Command (AFSPC). Because Air Force Space Command was redesignated as Space Force, any projects that were AFSPC are now USSF. It's true that, as I'm writing this, very few people are actually members of the USSF (it might actually be a single person: the Chief of Space Operations). However, there are plenty of people assigned to the USSF: everyone who was assigned to AFSPC is now assigned to the USSF (they just aren't yet members of the USSF while the military figures out who to transfer, who to retrain, and who to keep in the USAF with a space specialty). Civilians work for the Department of the Air Force (which is the parent of both services), so they only need to change their business cards.
The X-37B was a project of Air Force Space Command, which was the part of the Air Force that specializes in space stuff. AFSPC is perfectly capable of handling rocket acquisition and development programs. Because the Space Force is the former AFSPC, the Space Force is also capable of handling those programs with its assigned personnel.