SOLVED: So I plugged the BTD into the windows machine and did a firmware update, the update software is available on sennheiser’s website. (Not sure if that was needed)
In Pop_OS! I went into sounds settings and made sure the sound output was to “Digital Output (S/PDIF) BTD 600.” If it’s set to “Analog Output BTD 600” the audio is compressed. I could have sworn that I had tried this before, but apparently not.
The same thing applies to the C81. Make sure it’s using the digital output to the Avantree C81, not the analog output to the C81.
Thank you! Turns out the problem was something else, but I learned about the dbus today too.