One advantage of Safari's implementation of tab groups is the ability to arrange them in your preferred order. This lets me arrange tab groups by broad topic (work-related tab groups, family-related tab groups, etc). I even did a hack-y thing where I created an empty tab group and named it "____________________" to create a separator between topics.
In Safari, this is accomplished in the sidebar. In Orion, perhaps a list of the user's tab groups would be best located in the History/Bookmarks/Reading List/Passwords/Extensions window, where they could be dragged around to set their order in the menu, like with bookmarks. Tab groups could also be renamed from there without having to be opened, which is another nice Safari feature.
By the way: what currently determines the order of the tab groups in the menu? It's not alphabetical, and it's not in order of their creation or modification—I can't figure it out.