Does anyone know whether the controller support means XInput only or whether it also supports DirectInput?

I don't know about that, but I know that that controller support is horribly bugged.
I tried to use my XBOX 360 controller and kept crashing the game, or playing several characters at once.

We have support for PS4, Xbox 360, Xbox one and other generic controllers, those should work just by plugging them in, if that's what you mean.

We have some DirectInput support, but I'm not well versed on this stuff, so I'm not sure how it's used.

- Maarit from Frozenbyte

I have simillar issues when I am using xinput controller (Gamesir T1s). Game crashes at start. When controller is plugged in when game is runnig, it crashes also.