I just found out about tab switching shortcuts and gave it a try. It sort of works, however, at least I on my Mac, have to first click with the mouse into the tab window, before the shortcut to move to the next or previous tab would even work. In order not to interrupt the workflow it would be great if tab switching would work more seamlessly.
Same for me, also I can only switch a few times before it stops working.
Tab switching like in the browser and finder would be highly desirable.