itch.io

Yes, Steam input for controllers will work as normal for non-Steam games added to your library

Great game but unfortunately the post-game Dream Hub is broken on Linux, text does not render in text boxes and even in the tab menu until the game is closed. Loading in from Continue without going to the Dream Hub first works fine and the game otherwise had no issues beyond minor lighting problems that kinda just are inherent to Unity

You can always manually add it to your Steam collection as a non-Steam game and run it through Proton, Steamgriddb has images for this game too if you're willing to go the extra mile. While that's not quite as nice as actually having it on Steam it's the next best thing

Surprisingly difficult for such a simple game