The latest macOS version is not compatible with AirPods Pro?
When using AirPods pro, the software doesn't work properly. The audio sounds pretty noisy and cannot be played and paused smoothly. Using other wired audio devices or the Windows version sounds all good. Is this some compatibility problem?

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I just tested with my own set of airpods pro and I don't see what you're describing. Do make sure your Default Input is NOT set to Airpods Pro or the sample rate will be forced to 8K which is the highest the microphone on those can support. That will certainly make playback sound worse.
I also notice that when my airpods are connected to my system, my bluetooth magic mouse feels more sluggish. I'm not sure if it's related, but it resolved as soon as I disconnected the airpods.