Project information: The goal of this project is to give you a desktop application that you can download and run games from itch.io with. Additionally you should be able to update games and get notified when games are updated. The goal is not to replace the itch.io website.
Having Itch in a Flatpak is even more important now, as Flatpaks on Flathub are the main way to install apps and (non-Steam) games on the Steam Deck.
The above-linked GitHub issue has a lot of interesting discussion, even long after it has been closed.
Meanwhile, there are workarounds (itch.io app on Steam Deck guide, showing off Celeste - YouTube) but they’re inelegant.
Hopefully Itch re-opens the issue and considers an official port to Flathub soon. (Otherwise, an unofficial port would still be very welcome.)