I'm pretty sure A2DP won't help you for calls – it's using the Bluetooth equivalent of TCP (i.e. it is connection-oriented and retransmit based), which is not appropriate for real-time communication.

You want mSBC support on HFP. Here's an open ticket for pulseaudio, for example: https://gitlab.freedesktop.org/pulseaudio/pulseaudio/-/merge...

Is there any plan in making it part of pulse audio shipped with Ubuntu? Is there a straight-fw way to install it somehow and enable high-quality calls for BT Headsets? I am sure that this is a very common issue especially now-days, where people have lots of calls instead of meetings due to COVID-19...

This I'm extremely interested in trying. I am willing to bet a lot of CSR (Qualcomm) based Bluetooth hardware (a LOT of headsets seem to be based on this) probably also supports FastStream - and this would be an absolute gamechanger for me.