That's the very first time I read "sanely-working-out-of-the-box" about Linux audio. I have a very different experience of course, such as "why do my BT headphones suddenly play everything at 8000hz sampling rate while I never asked for this and why the UI won't let me switch it back to 24khz ?".
This happens exactly the same for instance on Mac or Windows with BT headphones, it's simply a fact of Bluetooth. If at any point you open an app that accesses the microphone of the earbuds / headphones, the format will downgrade from high-quality, playback only BT profile to a low-quality duplex profile. There's no high quality duplex audio profile in the Bluetooth protocol yet afaik, and certainly not implemented by any vendor. Just do t use Bluetooth if you care about sound quality is the answer.
Sounds like HFP. For me on Ubuntu you can choose between audio playback profile and HFP in the sound settings ui, but maybe you have an app running that is changing that setting.
(Apologies for injecting advice into a grumbling thread)