Firefox just added support for tab groups (You asked, we built it: Firefox tab groups are here ), and Chrome has had them for a while (chrome.tabGroups | API | Chrome for Developers).
Currently, Stardown treats tabs in a tab group the same as tabs outside a tab group; it doesn't do anything special for them.
When the user copies links for all tabs using Stardown, the output should include group names and indent the tab links, if possible.