@matigo A strange fix was applied. Searching Apple Support forums I discovered it's possible to invoke a Bluetooth debug setting by holding down the shift & option buttons while clicking on Bluetooth in the menubar. From there, "if BT is available" you can reset the Bluetooth module.
The trick was to get the module recognised. I created a very temporary new user account & found Bluetooth worked when logged into it. So I reset the module from that account, logged out then back into the regular user account. Bluetooth now works!