I think I found a work around.
I went through all the normal restarts and resets including the SMC and shutting down the Wifi.
Tried the Debug command for Bluetooth. Didn't work the first time. then I did the following:
I stood on one leg, patted my head and....JK.
I unplugged all my peripherals, then...
- Held Shift+Option and click on the Bluetooth menu in the Mac menu bar.
- Clicked Debug and select Remove all devices.
- Clicked Debug again and select Reset the Bluetooth module.
- Restarted my Mac.
- Reconnect each of your Bluetooth devices.
When the Mac restarted this time, I could see number of items on the bluetooth menu, but it would not connect them or identify them at first. I removed each one, one at a time, from the Bluetooth preferences screen. Made sure all my bluetooth was off, then set them to pairing mode one at a time. It took a few moments, but the mouse was recognised, then the keyboard etc.
You might have to debug a few times. I think three ended up being the magic number for me.