Just to add another datapoint, I've happily used a Logitech MX Master 2 alongside Airpod Pros, both connected using Bluetooth, to either an M1 MacBook Air or a Microsoft Surface. Is it an issue with just AirPods rather than Pros?
I have two mx master 3's on my desk, and no problems while using the sony wf1000 xm4's which also tend to saturate bluetooth bandwidth.
My money is on Apple doing something non standard, not Logi.