This is definitely an app/service issue and not related to the OS, plenty evidence of the issue being reported across the web from Android to iOS and multiple device variants and bluetooth accessories. If this was OS related it would impact other apps too.
Discussion
I would tend to agree, likely something in the way the app uses the OS audio drivers. I had an identical Pixel 6 that worked fine, bought this one to put Graphene on fresh, and it has never worked. Everything else has been great, though. I appreciate you talking me into Graphene, or at least pointing me at resources that were convincing.