Quiz

The only section I know of outside the Course Sections is a section course block with just shows a menu that allows you to jump to a section inside a course. That block never made any sense to me as my courses rarely go beyond 5 sections anyway. I only ever put labels into section descriptors with small images left or right aligned, and links to all the required work are often inside the label, so never used it. 

You can find out if there is any development in this area, look at the Moodle Roadmap and in Moodle Tracker specifically at Quiz developments. That might give some proof of something, or some ideas that you could build on. In any case, I suspect that the word "sections" may be too generic and "groups" may be restricted, so think about what it is you really want and work it through that way calling whatever you want. Make your development and see if you can get it working as a plugin for the quiz module. Worry about the niceties later if you are starting from scratch.   

When you say "Sections" do you mean section headings as added to new pages of the quiz as here (direct link) https://docs.moodle.org/en/Building_Quiz#Quiz_layout ? 

I am moving this to the Quiz forum...

Sections work (normally). You can try it at https://qa.moodle.net/course/view.php?id=2#section-9 (but remember that you can only edit the layout of a quiz if there are no attempts, so you may need to delete the attempts on the demo site to try it.)