Right, I’ve found the smoking gun but I still don’t know what the problem is. I was fishing around in the forums and somebody mentioned udev so I thought I’d take a look at my rules. I found a random rule I didn’t recognise and it seemed to be messing with my GPU permissions. I looked it up and it turned out to be from NoMachine, which I’d recently uninstalled. Other people had been having issues after uninstalling it as well. I reinstalled NoMachine from the rpm I’d not deleted, restarted, and suddenly everything’s working again.
So nomachine_8.11.3_4_x86_64.rpm had caused all my problems, and I guess it messes something up when it’s uninstalled. I need to track down the problem now but I’m glad I at least have a solution even if it’s a workaround.
Update
For the record it’s something to do with this bug:
https://kb.nomachine.com/TR04V11131
That says that if you’ve enabled GPU rendering in the NoMachine server, and then uninstalled NM, you have to delete the udev rule to fix things. I’ve deleted that rule and disabled GPU rendering before uninstalling but neither of them let me use my GPU without NoMachine installed. I guess I’ll have to wait for them to fix it or give me a solution.
Thanks for all your help.