Dunno how but in some way I managed to fix this thing twice, right after software update.
The last time I made it on mi8 miui EU 10.0.11.0
The only thing I can remember I've done is:
1.i reported the issue with the report bug section in the phone preferences.
2. I tryed several times to turn the Bluetooth on
3.i totally closed the Mi fit application normally running locked in background.
I then tryed to reactivate Bluetooth and then rebooted.
4.after reboot I turned on Bluetooth (was already on) then turned on airplane mode and then off and Bluetooth came back to work automatically.
Let me know if something works for you!