I've played around seven hours now on my Steam Deck and used Bottles instead of adding the exe as a non-steam game directly. The default Gaming container in Bottles works perfectly with no extra faff, and then you can add as non-steam game from Bottles after configuring the flatpak permissions correctly as per the Bottles documentation.
For controls I currently have left and right triggers secondary and primary click respectively and the right trackpad as mouse for pencilmarks, View as reset and Select as pause / unpause, D-pad as direction, X for the X action, A as jump, B as undo, and regular press Y to toggle run and hold Y to walk. I haven't gotten to the part of the game where other actions are introduced but I'll revise and publish the layout when complete
this game has a beautiful soul