I solved this problem by #2 solution from this link https://piunikaweb.com/2021/04/12/macos-big-sur-bluetooth-connectivity-issues-workarounds/ But just by resetting the Bluetooth module alone, it doesn't work for me. I had to also click on Factory Reset All Connected Devices and then restart the mac. And now my Airpods 3 worked on my Big Sur Mac!