I had the same problems with the buttons being wrong when I connected it to my phone using X-input. Once I connected it to my phone using the Android, "Start + B" mode, it worked well with all of the buttons being correct.
@Hyawatta So you were able to connect it to your chromebook using Start+B and stadia recognized it? (via bluetooth?)
What chromebook are you using? It doesn't get detected on my pixelbook.