So I’ve determined that my Logitech Mx Master 3s and/or Mx Keys is what is waking up my sleeping Mac. The screens will shut down as per the settings dictate, but they will turn on again seemingly randomly, and then stay on. I’m sure the Logitech is the cause. What I’m not sure of is how to use the display off signal as a trigger to disable BT. If it is off (or the Mxs are off), the computer does not wake up / fire up the screens. What I’m looking for then is an automated method for shutting down BT, thereby keeping the displays off. The laptop stays open all the time, so it’s easy enough to wake / reenable BT with the trackpad. I’m not too experienced with Automations/Shortcuts so I don’t even know if they are the correct tool, but I have yet to find any BT control in either. Any ideas?
Why not use the dongle, I haven’t experienced any issues with waking when the dongle is used.
‘Bluesnooze’ will do this for you, but you will lose the wake with apple watch feature.
A utility blueutil can be called as a shell script.
The Keyboard Maestro forum has a few other recommendations for automation. Do a search for (toggle) bluetooth.
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JJW
Dongle not an option - hence the BT inquiry.
Also, Claude suggested Bluesnooze too, but after a problematic install, admitted “a known bug with Bluesnooze on M1 Macs and newer macOS versions.” 
The Sleepwatcher + Blueutil did the trick. BT is switched off as per Control Center, and doesn’t wake up via mouse/keyboard. I have to manually reconnect, but it’s much easier remembering that than to shut it off in the first place. 