The Space Force is now responsible for all DOD launches. However I believe that the payload itself still belongs to the Air Force Rapid Capabilities Office. Most of the people operating it may be "on loan" to the Space Force, but aren't actually members yet (I think there's only ~100 people so far in the Space Force)
It is transferred to the space force - the launch name is USSF-7 (https://www.ulalaunch.com/missions/atlas-v-ussf-7). The Space Force operates out of the Department of the Air Force (like how the Marine Corp operates out of the Department of the Navy), so it's it's civilian head is still the Secretary of the Air Force - it's military head is the Chief of Space Operations.
Given the frequency and consistency of narrative with which it appears in the press, at this stage I'm convinced it's an empty UAV used entirely for some marketing purpose
Based on what this talk indicates, the US Government is doing some questionable(...) things in terms of signals intelligence in space.
We probably won't know what X37-B is doing in space for years but I imagine they will have at least tried to do some big brother exercises. The US/Western Intelligence community effectively treats all communications as fair game - they always have (e.g. MI5 were capturing encryption keys from neutral embassies using microphones in the ~50/60s) they just possess the means to do it efficiently at large scale now.
I imagine a large part of its mission is also just testing military equipment that can't go on the ISS but that's not as sexy.
They're doing some questionable sigint things I'm sure, but you don't need reentry and reusability for that. The most likely use-case is for testing components to use in conventional satellites.
