Ero Hunters from Itch (updated, latest available, not sure if it's 1.0 or 0.9.7) works on Steam Deck like a charm (with ProtonGE 10-25).
Version 1.0.0 MonsterGirl Hunters from Steam doesn't launch on SteamDeck. Crashes after "Godette engine " intro screen (sometimes after resolution change attempt if it's set to "default " as I see game tries to set higher resolution, as after second intro screen fits only 80%, so probably it tries to set 1080p, bigger than SteamDeck 720p, with 100% scaling which pushes part of image outside of visible area) . Without ProtonGE, with ProtonGE, without patch, with patch, with default resolution and manually set native resolution, nothing helps.
Tried compatibility mode as well, not sure what it changes but it didn't helped as well.
Unfortunate. Was glad I could launch and update via Steam natively, but it seems it's not ready for SteamDeck yet.