I also find it a little bit confusing that the parent of a tab group is a regular tab, and would like to have "vertical" separators.
The way I have solved it for now is having a local html file that changes its own title via JS depending on the params received. If I want to create a vertical tab separator, I visit that file and rename the param, get a new tab title and then group the related tabs within it.
Of course, the new UI looks awesome!