Agreed! Here's my current `userChrome.css` to hide the tab bar when Sidebery is open, IIRC adapted from their repo because theirs didn't work fully for me. Admittedly this is hacked together, it was mostly just trial and error, but it works!
To make it work only when Sidebery is open, make sure you add a preface value in the Sidebery settings and use the same value in the css above; in my case I just use an invisible character. Couple it with Ctrl-E keybind to toggle the Sidebery panel, and it's been a big quality of life improvement for me.