Controller input not passed to game, working in Steam menus

Running the latest version of CachyOS-Handheld, on a recent desktop build (transplanted a 3900x and a 9060XT into a Lian Li A3 case as a couch gaming PC). Only had it running 2 days, so never worked / no rollback point.

Both my controllers (XBox One S via XBox dongle, 8BitDo Ultimate 2 (tested in both X/Dinput modes) work fine in the steam menus in big picture, test tools in the OS etc. They enumerate properly, Steam displays the right controller (Your 8BitDo... uses this mapping...) at game start. Once in Proton games, the controller no longer works, the game gives the keyboard guides on screen as if it can't see a controller at all.

Linux game(s?) work fine - I've tried HL2 which works great.

I've tried multiple versions of proton - the default Experimental and Hotfix, the cachyos-proton-SLR versions, and Proton-GE versions, same issue on all, so I assume its not a proton regression (as has been seen before back in February). Tried both with and without steam input, on both controllers

Start by reproducing the issue with the Xbox One S and 8BitDo Ultimate 2 controllers in the reported Proton games, comparing Steam menus and the working Linux game HL2. Check behavior with Steam Input enabled and disabled across the listed Proton versions; done means controller input is recognized in Proton games as well as Steam.

Written by the indexing model from the issue text.