If you have not tried these steps already, please try these steps.
Try new batteries.
Reset SMC: How to reset the SMC of your Mac - Apple Support Choose the appropriate method.
Quote:
Resetting the system management controller (SMC) can resolve certain issues related to power, battery, fans, and other features.
Startup in Safe mode. https://support.apple.com/en-gb/HT201262 Choose the appropriate method.
To leave Safe Mode, choose “Restart” at the bottom.
Quote:
Safe mode prevents your Mac from loading certain software when it starts up, including login items,
system extensions not required by macOS,
and fonts not installed by macOS. It also does a basic check of your startup disk,
similar to using First Aid in Disk Utility.
And it deletes some system caches, including font caches and the kernel cache,
which will be created again automatically as needed.
Try it again.
https://support.apple.com/guide/mac-help/connect-a-bluetooth-device-blth1004/mac