Monterey 12.5 not sleeping

Thanks for the reply. I have NO "cleaners, optimizers, antivirus, or VPN apps installed other than free Malwarebytes, which I understand is known to be safe and is widely recommended.

By trial and error, I found out exactly what is waking my iMac. I have Logitech MX-series keyboard and mouse. They're the same ones I had been using before I reformatted the HD and reinstalled Monterey when there was no problem with sleep mode, but I think that the previous version was 12.4, and this time I ended up with 12.5.

If I simply turn OFF both the mouse and keyboard and then put the iMac to sleep with a little $4 USB mouse OR the Apple Magic Mouse (also connected by BT), the computer sleeps perfectly normally. Interestingly, switching either the MX mouse or the MX Keys keyboard to its "ON" position instantly wakes the computer with both of them paired.

I suppose it could be a bug introduced with macOS 12.5 but it doesn't seem to affect Bluetooth-connected Apple peripherals, just the ones from Logitech. I'll do the upgrade to 12.5.1 and post results here.

Thanks for the smart suggestions. I did check that it's scheduled to sleep. It always was, but that wasn't the problem. The problem was that when it was put to sleep manually, it would wake up again within 40 seconds, and when it entered scheduled sleep, it woke in less than 40 seconds. It does have wake on LAN enabled, but that's not the problem, either. It doesn't sleep with Logitech bluetooth-connected peripherals -- namely, keyboard and mouse. If those are removed, it sleeps perfectly. Further experimentation to follow.

Old Toad, I read you loud and clear. I had already told my brother (my partner in crime in performing the upgrade from the HD to the PCIe SSD) that shutting down was what I was going to do, but I'm enough of a perfectionist that I didn't want to let this problem go unsolved.

Interestingly, after the update to Monterey 12.5.1, as suggested by leroydouglas, the iMac did put itself into sleep mode per the schedule and criteria in System Preferences/Power. It stayed in sleep for 12 hours until I tapped the keyboard just now. However, and very mysteriously, if I try to enable sleep when leaving the area for a while, it still wakes up within 40 seconds after entering sleep. As before the OS update, simply turning off the Logitech keyboard and mouse makes it stay in sleep.

In a recent macOS update, Apple removed the option for preventing bluetooth devices from waking the computer, which would probably solve my problem if I still had that option. But I'm now suspecting that when it follows the Power plan for entering sleep, the OS does perform that function, making the computer ignore the bluetooth signal but allowing it to wake when it senses a keystroke or mouse click. I figure that it doesn't have time to do that or is not programmed to do that when the user sleeps it manually. It's what would explain this strange behavior. I think I can live with that

But for now, I'll probably follow your advice and shut down at the end of the day because the iMac boots so fast that it's not inconvenient to do that. In fact that was my practice for 20 years before switching from the Windows world to the Apple universe.