M1 iMac will not sleep

I have an M1 iMac (running the current version of MacOS Ventura) that I purchased when they first came out in 2021. It has worked perfectly for most of that time. But for the past few months I have had a persistent issue with the iMac not wanting to sleep.

When I select sleep from the pulldown menu, the screen briefly blinks out – as if the computer is going to sleep – and then it immediately comes back on. Sometimes it will go off after 2-3 attempted to put it to sleep. Other times I could sit there, repeatedly trying to put it to sleep but it just refuses. Naturally, this is pretty frustrating, sometimes requiring me to completely shut down the iMac.

I have gone through all of the troubleshooting I can think of, based on online research. I have checked the energy settings (which are limited on this OS). I have opened Activity Monitor to see if there is something preventing sleep. But this problem persists when Activity Monitor shows nothing preventing sleep. Thinking that there might be something nefarious installed without my knowledge, I have installed and run virus and malware apps. Their reports come back clean. I have even done a clean install of the OS. And yet the issue persists. Lastly, I'm taking care to immediately remove my hand from the mouse as soon as I select sleep (so it is not some subtle device input that is instantly waking the iMac.)

Beyond all of that, I'm stumped. If anyone has any theories about what else I might try I'd love to hear it.

PS: I have had some ongoing issues with AirPods Pro 2 and AirPods Max constantly disconnecting from this iMac. One second I'll be sitting there working, listening to iTunes or running a movie in the background, and the audio abruptly disconnects (while still appearing to be connected in the menu bar). I mention that in the event that there might be a hardware issue with Bluetooth that might be related to both issues.