The game does seem to have some semblance of support for Playstation controllers but the button mapping is all sorts of broken. It will recognize it but if all the buttons seem to be scrambled to some degree.
You can use DS4Windows or Steam to get the controller to work, but you will no longer have Playstation button prompts as it will think the controller is a Xbox controller.
More information here: https://steamcommunity.com/app/775500/discussions/0/3056237435833637209/?ctp=2
As far as I know, there isn't currently a way to both use a Playstation controller AND get the correct button prompts. I should probably also note that I have my DualSense controller connected via Bluetooth. I'm not sure if connecting it via cable would make a difference.