Tab Groups are currently implemented in Chrome such that closing all of the browser's windows (or even just a window with a tab group in it) does not eliminate the list of existing tab groups; they're saved, and the user can click on a tab group in the list and respawn the tabs in that tab group. If I recall correctly, Brave implements it this way too, as does Safari (though it looks different, obviously).
To me, this is the killer-feature aspect of Tab Groups: they're like temporary bookmarks, so even if my browser crashes, I don't lose what I was working on, but I don't have to go to the trouble of saving (and updating) a bunch of bookmarks to get that effect for things that I only want to save temporarily. It would be great if Firefox added this ability as well.
Thanks!