Thanks for playing, passing by and taking the time to report this issue. That's a really weird bug. I did not experience such issue on Linux. Which Linux distribution and controller are you using, please?
I'm using SteamOS on a Steam Deck. Both the Steam Deck's internal controller, and an external bluetooth controller are affected. (I don't have the game on Steam, I got it here from a bundle.)
I've run it from the desktop and in Steam using the Steam Linux Runtime, and both result in the same problem with the controls.
Something strange I noticed is that the improperly mapped inputs seem to align with what happens when I run a game designed for DInput controllers while using an XInput controller, with the exception that the face buttons (ABXY) all work correctly.
I don't have a PlayStation controller, but I think that if I tried to use one, it would work correctly.