Any master source for which addons do or don't have GAMEPAD mode support?
 

Unfortunately there isn't a search function for an Addon Comments section so I can't be completely sure if not specifically stated in the Addon Info tab.

Is there any repository of which addons do or don't have GAMEPAD mode support noted by the authors?

I'm trying to answer for a few on a ESOReddit thread by just searching the addon tabs.

Nope, sorry.

You could ask for a Gamepad section in the esoui forums > Site Forums > site Suggestions.