This is not Tab Groups. There is no functionality that I expected from an addon that claims to be inspired by it. I have found no option to skip the "groups menu" dropdown and go straight into the management screen, and further the groups management screen opens itself into a tab or a window depending on the setting you have set, yet neither of these options were the way the original Tab Groups worked. It used to be that it seemingly created a navigation bar-less fullscreen window with the tabs displayed. I don't know what the limitations of quantum's haphazardly asinine addon system are, but that's rather disappointing. I don't like the current standing separate window view, nor the tab version. Very clunky to use.
Further, although explicitly stated as being planned for a future update, you cannot freely arrange the tab groups in the grid view, which is unfortunate.
This was not worth updating from Firefox V56.0.2 for, though unfortunately I was forced into doing so by the fact that many webpages have begun to discontinue support for the legacy version of Firefox. I am left with no other choice.
Edit: Boosting up to four stars because I found an amazing workaround. You can right click > PIN the "Manage Groups" tab and then, voila, there is an always-present button you can press to bring you right to the overview screen. It's on the left, not the right, but hey it's better than being forced to use that menu.