TLDR if you use Ubuntu 19.10 or 20.04:

sudo add-apt-repository ppa:berglh/pulseaudio-a2dp

sudo apt update

sudo apt install pulseaudio-modules-bt libldac

TLDR if you use Ubuntu 18.04, 18.10, or 19.04:

sudo add-apt-repository ppa:eh5/pulseaudio-a2dp

sudo apt-get update

sudo apt-get install pulseaudio libavcodec58 libldac pulseaudio-modules-bt

Reboot and enjoy much better sound. You may also need to make sure it is actually using AAC:

Connect the headset, go to the bluetooth panel and set the Audio Profile to a2p_sink_aac