More specifically, Firefox is updating itself in that situation so it knows not to do anything until startup/shutdown. When the you-have-to-restart tab appears

More specifically, Firefox is updating itself in that situation so it knows not to do anything until startup/shutdown. When the you-have-to-restart tab appears, it's because Firefox didn't do the update, something external on linux (apt or snap or something) did it in a way Firefox can't handle.