Currently I see family, size, weight, line-height in the font tab of dev tools.
Why not go all the way and include everything listed in https://developer.mozilla.org/en-US/docs/Web/CSS/font ?
It's an interesting idea. I just wanted to mention that the DevTools team has its own forum and your idea might get more prompt attention over there:
https://discourse.mozilla.org/c/devtools/213
never-displayed