Bluetooth not available on 10.15.7 Catalina on a late 2012 Mac Mini

How do I identify the cause of "Bluetooth not available" state on 10.15.7 Catalina on a late 2012 Mac Mini with 16GB memory?

I have a no-name rechargeable keyboard and Logitech MX 3 paired with the system.

The keyboard has a built-in power saving feature that disconnects it after a certain time, but one can reconnect it by touching any key.

The MX 3 has a power switch, otherwise always connected.

Sometimes, for no reason I can see in the logs or in Console, the Bluetooth module gets turned off and nothing I can do through BT Explorer or other actions to turn it back on.

The only thing that resets it is restarting the system itself.

It usually happens when neither the mouse, nor the keyboard are in use for an extended period of time, like when the screen is locked overnight.

As there's no longer any support for Catalina, I've done the SMC reset after removing the BT .plist files and ran EthreCheck to see anything obvious shows up, but nothing.

As I read similar posts, the nature of the Bluetooth system becoming disabled could be either hardware, or software. If hardware, a reboot shouldn't allow the BT system to function again, no? If software, where to start for culprits that would knock out bluetoothd? When I use the Shift + Option on the blutooth menu, there's no option for turning on or off debug logging. Only Debug=>Reset.. etc. options.