I recently installed the official release of Big Sur and auto ear detection feature of my AirPods stopped working which was earlier working on Catalina.
Auto ear detection of AirPods not working on Big Sur
I'm having the same problem. Since Big Sur, when I take my AirPods Pro out on my MacBook Pro, it no longer pauses the audio.
Go to bluetooth settings, choose your AirPods, select options and there you can activate it. Hope that helps.