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

Literally any file can be added to Steam by right clicking and selecting "add to Steam"

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.

Non-steamlaunchers can make it easier https://github.com/moraroy/NonSteamLaunchers-On-Steam-Deck