That's very strange, I just tried it on my end and I do not have the same problem's.
When you click vibrate, whether through the gamepad or via the onscreen toggle, does the toggle show the heart or does nothing happen?
If you have the Steering Wheel Support DLC you can try removing that and making sure the Steering Wheel Support toggle in the Controls is turned off.
If you have another gamepad you can try that, otherwise maybe test to see if the vibration works in other games to make sure its not a gamepad issue?
If you go to Controls > Remap Controls you can see if the vibration button is set to the correct button.
If you have Steam running you could try quitting and making sure its not running.
If you go to troubleshooting you can fully reset the app which might help if something's gone wrong.
Otherwise last thing I can think of is to make sure your gamepad is plugged in, then go to "Check for updates" in Windows (You can search for it in the search bar in your taskbar), make sure your computer is up to date and also check for optional updates as there may be one to get your gamepad working correctly.