If you have a problem with your bluetooth connectivity on linux. Below is the solution that worked for me. So I have a logitech Triathlon mouse that connects via bluetooth. This is an on-board bluetooth module. The problem started when I updated to version 20.04 of linux. After few seconds of inactivity, the bluetooth seems to sleep or suspend until you move your mouse again. This is very annoying in my case. So I find some solutions on the web, I've tried bunch of them But this one fixed it.
https://support.system76.com/articles/bluetooth/
This post all helps on a lot of bluetooth issues
https://medium.com/@overcode/fixing-bluetooth-in-ubuntu-pop-os-18-04-d4b8dbf7ddd6
Hope that helps.