For what it’s worth, I was running into this exact issue with a fresh install of Volumio 3.631 on a Pi 4, using a 32GB microSD card. I wrote the downloaded image to the SD card with dd, and the system was setting itself up and generally working just fine, besides this weird problem.
Fortunately, I found this thread and was able to fix it with @akelge’s solution (thanks! Having to mount the partition to be able to use resize2fs is not very intuitive! 
)
What was interesting, and maybe useful for debugging the issue: I had previously briefly played with Volumio in a VirtualBox setup (just a quick test before purchasing the Pi), and I probably had the same issue there – at least I got the same “No space left on device” error while trying to set up audio sources (IIRC), but I didn’t look into it further at the time.
