We're experiencing same technical difficulties on several bluetooth headsets, My Logitech H600 worked perfectly fine until a few weeks ago.
Windows 10.1909.2020-07 cumulative patches/updates have been deployed by IT on July 21st on my computer and it kind of looks like it fits the time it stopped working properly for most of us.
KB4565483, KB4565554 and KB4565633 (.Net framework) were among the items installed.
I had Windows 10.2004 pending in my Software Center.
I'm applying that upgrade and we'll see what happens.
But this issue has got me buying bluetooth dongles thinking they were flawed or missing some features.
Only to realize now, that it's been a Windows Issue all along. OR that it seems to be.
I can confirm it does the same with Google Hangouts, Discord or any other communication software that uses the PC's microphone device.
I even had some issues with my Turtle Beach PX22, which is wired by the way (1xUSB, 1xAudio), where I couldn't use the usb microphone and speakers in hangout while having game sounds going through the audio jack. Which worked perfectly well before.
I got it to work again but only after I installed Realtek sound manager and have it manage the audio I/O instead of Windows.