With the horizontal tab layout, you can drag-and-drop the group name to move the whole group, same as singular tab. Although the first time I tried it it didn't work, now that I keep trying with different click timing etc it seems reliable - not sure if there's maybe a drag handling bug hiding in there somewhere.
I've only enabled tab groups on my profile after updating to 138 today. That first attempt where drag-and-drop didn't work was already on 138. But I can't reproduce it anymore, so I assume that was a fluke. Looks good so far!