sorry for the late answer. I don't know exactly which chatpad you have, but Stadia-compatible gamepads and screens are listed in this article. If the one you plan to use it not mentioned there, it might be not supported. I also don't believe Google has an own one, if theys would have one, you could buy it online in the Google Store.
Therefore if your chatpad is not supported, I would recommend to submit this feedback in the Stadia app or on stadia.google.com by tapping your profile icon in the top-right, then navigating to the "Feedback" section. The Stadia team reads every piece of feedback, so this is the best way to get your voice heard!