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.