I can see the controller being recognized in the menus but no keypress is detected. the controller shows as something like "PS4 Dualshock controller (custom)". I also tried to stop steam just in case but nothing changed

Running linux here with the same problem. Re-connect the DS4 controller *after* the game started worked for me. Also try ds4drv (or DS4Windows? if using windows) to map your ds4's DInput to XInput compatible API.