If it's not a game you can redeem through Steam, then install through desktop mode and add it to your list of games in Steam (add non-steam game). That will let you access it through the normal Steam OS
this post was submitted on 29 Nov 2023
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Lutris integrates with itch.io these days, I haven't used it extensively but it seems robust enough. It should also support your local DRM free games and whatnot.
GameHub supports Humble Bundle and itch.io though I haven't tried it on Steam Deck yet.
Edit: Unfortunately the appimage/flatpak packages are pretty borked and installing via pacman would be more trouble than it's worth.
Thank you for looking it up and helping out.