27" iMac 2020 turns off Bluetooth during sleep after switching users
For the past month or so, my iMac has been spontaneously turning off Bluetooth during sleep after switching users, so that when I try to wake it up the next morning, I can't. I have to plug in an old USB mouse and plug in the Bluetooth keyboard to one of the USB ports on the iMac, as though charging, then I can log in and turn the Bluetooth back on.
I'm running macOS Big Sur (11.6.4) on an iMac Retina 5K, 27-inch, 2020 model with the Intel Core i7 processor, which I purchased new from Apple in March 2021, so it isn't even a year old yet. Rebooting didn't help. I've also disconnected the power cord for several seconds, which supposedly resets the PMU, in case that might help, but it didn't.
Would anyone have any ideas as to how to correct this bizarre problem? Should I consider upgrading to macOS Monterey? I've read about compatibility and speed concerns with that OS and Intel processors, so I've been hesitant, but maybe I should bite the bullet.
Thanks!
iMac 27″, OS X 10.11