Xinput Controller,
Elecom JC-U4013S
All other buttons and remapping works. Would have liked the vibration for the fishing game though.

I've been having this problem too. I tried multiple controllers (8bitdo, DualSense, Xbox Series) and rumble works with none of them. Doesn't matter if they are connected wirelessly or with USB.

Try using a dinput controller. If the dinput controller has a vibration function, it should work.

My Controller has both a D-input and X-input switch on it, so I flicked the switch, however the game does not vibrate it.
I went into controller settings and confirmed that it does actually vibrate, so the controller itself is not broken in that respect.