Interesting, thank you for getting back to me and apologies for the issues you're facing. I don't have a Steam Deck myself so it's difficult to test, but I'm in contact with a few people that do have one so I can get them to test it. Thanks!
I just figured something out. I haven't been using the Deck on the go lately so I'm always in desktop mode.
I tried switching to to game mode (it's a more game console like mode if you aren't familiar with Deck terminology) and running Revamped that way. And the Logitech controller worked. After switching back to desktop mode to double check, controller won't work again.
That is strange. All other games I've been running through the itch client have been controlling the same whether in game mode or desktop mode. It's odd that in Revamped controllers won't work properly in desktop mode when they do in game mode.
Unfortunately it's also pretty inconvenient, because game mode doesn't let you have a browser or Discord open in the background. Or anything else really. If you aren't using the Deck on the go then being forced to use game mode for something is a real drawback.
The only other time I've seen a difference in a game between desktop vs game mode is there's two games I have (Steam games, not itch ones) that for some reason won't launch in desktop mode even though they run fine in game mode.
Anyway, long story short: If someone's going to help test I can give some details that will help replicate everything.
I'm running Revamped through the itch.io client in Desktop mode. I'm launching the itch client using Lutris (through a shortcut in Steam created by Lutris). I remember that the itch client wasn't running on Steam Deck until I started running it through Lutris. And of course controllers aren't working right in desktop mode, whether external or the Deck's own controls.
That should replicate everything.
One thing I noticed while testing in game mode is that the default Revamped control scheme doesn't let you change the sensitivity of looking around. Pressing the pencil icon to edit either of the two default control schemes does nothing, so there's no way to change it.
That can be gotten around by making a new control scheme set to fps and adjusting the analog look sensitivity there. But having to to make a new control scheme to do that is a bit silly.