Mac OS Monterey 12.3.1 Bluetooth On/Off
As a former thread (Monterey and Bluetooth - Apple Community) that posed a related question that remained unanswered is now automatically closed, I am starting a new thread along with its resolution as I cannot find any helpful answers to the original. I do wish Apple would review unanswered questions before closing.
An answer: Under Mac OS Monterey (at least for 12.3.1), Bluetooth on/off functions are now under a security lock that requires authentication. The problem is that the lock/unlock icon that leads to this authentication is not displayed without the Shift-Option access, and once it is displayed, it is so tiny you may not notice it. So:
1) Holding the Shift & Option keys down click on the Bluetooth icon (either on the taskbar, if it is displayed), or from the main page of System Preferences.
2) This will display the tiny lock icon to the right of the "Turn Bluetooth On [Off]" button.
3) Click on the tiny lock, which should initiate authentication (fingerprint or password).
4) Now the button is enabled and you can turn BT on and off.
Note that some of the prior functions such as resetting the entire BT system, or removing all paired BT devices are no longer available even with this method under Monterey.
Cheers.
MacBook Air (2020 or later)