I got it to work to drag-and-drop and reorder tags!
In short, first, CLICK the left-menu item that shows the tag icon and says 'Tags'. That pops out a drawer menu for tags specifically. You can drag-and-drop from that menu specifically! Video included. Worked both on the latest desktop app (version 10.5.7) AND web app (version 10.5.6).
Dragging and ordering tags from this screen: no
Dragging and ordering tags from this screen: yes!!