2020 iMac 12.1 won't stay asleep, quickly wakes up and stays awake indefinitely

What mouse/pointing device and keyboard are you using?

In Monterey Logitech device seem to way the a Mac.

As a test can you disconnect your external drive and other devices?

Reset SMC and NVRAM (if applicable).

How to reset the SMC of your Mac - Apple Support

Reset NVRAM or PRAM on your Mac - Apple Support

Then try booting to Safe Mode. That boot up takes minutes and clears caches and other things that may resolve your problem.

How to use safe mode on your Mac - Apple Support

A lot of times just boot to Safe Mode followed by normal boot resolves problems.

Last, download and run this app so we can find more information about your installation.

https://etrecheck.com/upgrade

It shows what is launched and other information and is very useful in finding causes of problems. After you first launch the app make sure you check Enable full disk access in the box in lower left.

After running the app use the app's feature to paste to clipboard. Then paste it in the text box for a reply in this forum click on the addition text icon. This is because the normal reply text box limits how much you can type.

Paste additional text box image

No personal identifiable information is contained if the app output. The app was written for a person who is contributor to these Apple Support Communities

I turned of my Logitech BlueTooth mouse. I also have a Mattias BlueTooth keyboard, but the computer still does not stay asleep even when it is powered and the MacBook Pro only uses a wired USB mouse and keyboard.

Changing the Power Adapter settings does not change this misbehavior, either. Have already had 1 call to Apple Support but didn't solve the issue.

There are reports from Off Apple Sites indicating the Wake and Sleep and Wake issue is related the any Bluetooth Keyboard and / or mount connected to the computer during this time frame.

Some have reported turning off Bluetooth on the computer before putting to sleep as a temporary workaround.