How to fix bluetooth problem?

Try to do SMC Reset as this will help for

General performance and functionality problems: abnormally sluggish behavior despite no CPU or disk usage, external ports not working, airport & Bluetooth aren’t showing up, external devices are not being found, etc

Apple says you shouldn’t reset the SMC without first trying other troubleshooting tasks, such as force-quitting problematic apps and restarting your Mac. However, Apple doesn’t mention any negative consequences of resetting the SMC, nor any way to determine for sure if the SMC is glitchy without resetting it and noticing that the problem went away. I’ve reset my Macs’ SMCs many times with no apparent ill effects, and on the occasion that did, in fact, turn out to be the solution to a problem.

How to do SMC Reset

Shut down and unplug your Mac. On the built-in keyboard, press and hold the Shift, Option, and Control keys on the left side and press the power button and hold all of these down for 10 seconds, then release the keys. Connect the power adapter and then turn the Mac on normally.