The only way to fix bluetooth problems with big sur is to wipe the disk ( you will lose all your data, but this is the only way to do this) and reinstall the original software that came with your mac ( mine is El Captian) and then install that. Once that is done, reinstall the software, once set up, go to the internet and search " older versions of macOS". Select Mojave and download it, then install it. Once set up, try repairing your bluetooth devices. do not upgrade to catalina or big sur. Ignore any update reminders ( expect those for Mojave). I am using my bluetooth speaker and it is working well. hope this helps for some of you that have bluetooth issues.