macOS Monterey Bluetooth "wake" option

I had the same problem with Monterey & Macbook Air with an unbranded bluetooth keyboard.

The problem went away after I connected the keyboard via the System Preferences / Keyboard / Set up Bluetooth Keyboard dialog rather than directly via the System Preferences / Bluetooth dialog. Subsequently the problem does not recur whichever method of connection.

Seems to be a more general problem, not just Logitech. I experience the same problem with a Microsoft Surface Ergonomic Keyboard and MacOS 12.1. Worked without any problems with Big Sur. Now if you type something, read something else for a little while and then want to continue typing you find it disconnected and the first two or three letters that you type are lost.

Yes, I know that this keyboard is not officially working with MacOS beyond 10. But still it is about the best ergonomic keyboard available, at least for my hands. And it worked with MacOS 11 before.

Just a suggestion for Logitech users: I prefer the Logitech specific transmission with their dongle (for MacOS).

The problem with your Logitech keyboard may be a Logitech problem since there are discussions here where Logitech keyboards and pointing device will periodically wake a Mac w/Monterey from sleep.

I may recall one problem in this forum with Yeti mic. Thee have been a few problems with a few USB drives seve ejecting but no general problem.

Are you fully updated to 12.1 released in late Dec.

Great idea, SJL-WOX! Thank you. I never tried it this way. However, the world is full of unexpected surprises. The Set up Bluetooth Keyboard dialog does not find the Microsoft Surface Ergonomic Keyboard, at least not with my iMac Pro (as well as with my very old Mac Pro) and MacOS 12.1. If I activate the pairing button of the keyboard the wheel continues to spin (no keyboard detected) until I stop the procedure after several minutes. Going back to the Bluetooth preferences it shows up (as "Ergonomic Keyboard", so it seems to be identified nicely) and wants to be connected (with a code). But nothing in the Bluetooth Keyboard Setup. - I admit that the Microsoft Surface Ergonomic Keyboard is a special beast. E.g. the Apple keyboard keeps its connection when going from Mac to Bootcamp and back whereas the Surface Keyboard needs to be paired again and again. But staying with MacOS everything was fine until and including BigSur.

Nevertheless your idea is at least a valid procedure, if the keyboard supports it. I have a small Hama keyboard that I sometimes use when traveling with iPhone or iPad. Press the Pairing button and there it is in the Bluetooth Keyboard Setup. It shows up with its address and after selection with its name. Unfortunately, I do not need this keyboard here.

Since about a week I am now "back to the future" with an USB ergonomic keyboard that is at least flat enough for my hands and it works under all circumstances.