Zoom cuts of bluetooth headphones completely

When I connect my AirPods Pro 2 to my Windows laptop, they work fine, I hear audio in all apps, I hear the test tone when I change volume in the Windows audio mixer. The moment Zoom opens, they stop playing. I cannot hear a thing in Zoom, I cannot hear a thing anywhere else, the headphones are effectively muted. This persists even if I kill zoom. If I disconnect and reconnect my headphones, audio works again, until Zoom is opened.

When this issue occurs, visual guides (meters) representing the audio playing in the system or Zoom app do indicate playback, but no audio is audible.

This happens only with Zoom, other communication apps are fine, repro rate on this is 100%. I am connected to correct headphones, the audio device is unmuted in the system. When these headphones are used without Zoom app, they work as expected.