I'll go ahead and say i use the itch.io launcher on steam deck, and it works great !! Really, its awesome !! The trick is... that i'm using the Windows launcher.
Do yourself a favor : execute some of the steps listed here on this page, except don't download the Linux flavor, but the Windows. Installing will be a little trickier, i don't remember all the steps, you will have to look for them on reddit for explanations ; but the basic idea is the one explained here : (after manually downloading the itch Windows launcher installer) add the downloaded installer to your Steam library as a non-Steam game, run installer, then (that's the tricky part which i don't remember) manually change the path that your steam library shortcut links to, to the path where the launcher has been installed.
But once that is done you'll have access to the itch launcher through steam library (it works in game mode as well) and you will be able to install the Windows versions of games, which work better on the deck than the Linux versions (this is true for most of the existing videogames : 99% of the time Windows versions work better on the Deck than their Linux port). Actually i have played a lot of games of different levels of polish, really few have really refused to work.