Well that sucked.
First, the area still is running on a long outdated rule about foreigners only being allowed to stay in 5 star hotels, and all the ones near where I needed to be were booked for some sort of local event. Initially, this was supposed to be something very easy to override by the local government contacts there, but it appears that hotel managers view those rules as more important than low level government officials. I got stuck somewhere around 100 km away. I know this rule for where foreigners could be parked overnight used to exist, but I've stayed in smaller hotels in 5 provinces with no issues. The actual current law seems to be something along the lines of hotels just needing to apply for permission. But everyone I talked to in Qinghai seemed to think this law was some immutable nationwide rule that was deeply carved onto a stone monument somewhere in Beijing back in 1949.
This was annoying and inconvenient, but sadly, it was just a foreshadowing of what was to come.
Then the local officials decided that although I was free to wander around anywhere I liked in Qinghai, I wasn't authorized to do anything involving the charity or interact with the sponsored students. I could, for example, accept an invitation to visit anyone's home (if such an invitation was offered), but was forbidden to visit the schools or homes of any of the students sponsored by the charity.
The visits start today. I was there to see the students. There was no point in remaining while I couldn't do what I was there for. I flew back yesterday.
Sadly, this whole fiasco was quite avoidable. The person in my charity group had been specifically asked to double-check if my lack of Chinese nationality would cause any possible issues. He didn't seem to think there would be any issues, so he didn't bother to ask his contacts in Qinghai or to even mention that a foreigner would be part of the team planning to visit the schools and homes of the students.
The two charity members who went to XJ fared better. Initially, the whole planeload of people was held in the capital for a few hours for additional Covid testing, but they still made it to the destination city in time to do all the planned visits.
In any event, I've got my wife checking to try to find the exact current and historical versions of the various rules about where foreigners can and can't legally stay. (She's just discovered that some hotels lack actual hotel licenses - instead they claim to be renting apartments on their official licenses and would have trouble registering a foreigner with the police for a typical hotel length of stay. This could be the source of some "hotels" rejecting foreigners.) She's also going to figure out who can give an absolute crystal clear ruling on just what having a green card does to any default foreigner restrictions on lodging.
I'm also going to make 200% sure I've got whatever local permissions I need all lined up far in advance before for the next charity trips to XJ and QH.