Sorry to hear about your issue. I don't have access to a Steam Deck to test, but on Windows, downloading the latest Itch build (40) and running it, and using the Itch client both work for me... and as far as I can remember, nothing really changed between the last 2 versions that would cause what you're seeing.
Can you try uninstalling and re-downloading the latest version in case the download somehow got corrupted?
Can you try the Demo version - which is built using the same code as the main version - and see if that works?
Does the Steam Deck have any kind of crash reporting or anything that might say what's happening?
If you want, you can respond via email: tim@axolstudio.com