All hotels have to report their guests to the local PSB, but some smaller hotels don’t (rules aren’t that enforced in China), but will avoid foreign guests because they easily bring attention from authorities. You can get away without reporting to the PSB in some way out places (like a hostel in the middle of nowhere I stayed in that lacked electricity beyond a simply hydro wheel), but those are rare, and not in big cities.

The rooms aren’t bugged. Most foreigners aren’t that special. Maybe they will big some special hotel that gets lots of diplomats? But most of us won’t stay in those.

China only start to recognize passport as identification a few years ago, previously a Chinese citizen can only use national id. It was just a lot extra work for the hotel if they don't have this system. No, you can get bugged, but by the state, maybe by some creeps.