USB-C headphones not working despite being listed as audio device

Solution 1:

Sounds to me like, a channel that is not seen by the user accessable puleaudio controls is muted.

Open a terminal:

cat /proc/asound/cards 
#Take note of what is there.

Run alsamixer:

alsamixer

You will now see a user interface. In this user interface, you can do the following:

Select your correct sound card using F6 and select F5 to see recording controls as well
Move around with left and right arrow keys.
Increase and decrease volume with up and down arrow keys.
Increase and decrease volume for left/right channel individually with "Q", "E", "Z", and "C" keys.
Mute/Unmute with the "M" key. An "MM" means muted, and "OO" means unmuted. Note that a bar can be 100% full but still be muted, so do check for this.
Exit from alsamixer with the Esc key. 

Solution 2:

I tried the solution from Michael Prokopec, but the audio channel was not muted. I found, however, that the applications trying to play audio were trying to use the "Built-in Audio Analog Stereo" device. USB headphones, or at least the Pixel Earbuds, register themselves as entirely separate audio devices. To get audio to play through the USB-C earbuds, I had to manually change the audio device in pavucontrol.