Fully Steam Deck Compatible! ːsteamthumbsupː
Long story short: the Steam Deck Compatibility Review process is a long one, with strong favouring to highly popular or anticipated games getting priority (fair enough!).
As such, after working through the sluggish task of UI development, I still need to wait for Valve to get around to testing Chase St before they give me a fancy green tick.
I have tested myself multiple times and can confirm that the game runs great on Steam Deck, and doesn't need any on-screen keyboard or Mouse/Tap input to navigate the menus. The default setting might still be incorrect, but swapping to a pre-set gamepad mapping sorts it out.
Thanks so much for considering Chase St, and good luck finding your way home while tucked up safely in your own bed...