Something before getting into A2DP codecs is to make sure your device is using A2DP and not HFP (headset mode). Many bluetooth headphones have a microphone built in so that they can be used in headset mode, and depending on your distro and your bluetooth card, the OS may default to HFP mode. In my case, Ubuntu required me to change the Bluetooth mode every time I connected a bluetooth headphone set up until the 19.10 update.
In my case I can't even use Bluetooth microphones, just the output mode. Apparently when switching from Bluez4 to Bluez5 this was dropped by all major distributions, which frankly baffles me.
Semi related: Is headset mode worth using for voice chats? Enabling it seems to cause noise and "incoming call" voice messages. I'm not sure if it's bad support for my specific hardware type (LE Bose QC35 II) or just bad HFP support in general.
HFP mode is not worth using for anything unless you are roleplaying a person from the 90s taking a phone call in the car.
The sound quality is truly awful in HFP mode, I can hardly understand what people are saying when in that mode and you sound horrible to everyone on the other side as well.