I just observed a very strange behaviour (Macbook Pro 13 Zoll, 2019, Big Sur Version 11.0.1): when I am using my bluetooth earphones (Jabra REVO a4.0.0), the Touch Bar Volume Slider Widget does not only change the output volume but also shifts the balance to "left" (can only hear on one side).
This however only happens when I have the bluetooth earphones connected, if I select the MacBook Pro Speaker this does not happen, only the output volume ist changed and the balance remains unchanged.
BTT doesn't really do much but tell the system to change the volume, it has no code to change the balance. As far as I know a system restart usually fixes this, but it can happen randomly again.
There are many macOS bugs without known workarounds
However the more information the more likely I can find a workaround for the issue. Can you observe this balance change in System Preferences => Sound => Output while you change the volume using the BTT slider?
Maybe I can grab the balance before changing the volume and then set it back to that value after changing the volume. I'll add that to the next alpha and let you know when it's online.
In general the API I'm using says it is setting the volume for all channels (left and right) to the same value. Maybe that doesn't work for some speakers, but I have no idea why it wouldn't...