Yeah so I found out that if you enable Desktop Site in the Google Chrome app on any Android or iPhone, you can play Stadia games on it. I played for about an hour with any real issues. So if you really want to play on your phone, but don't have an issue, there is a way.
What controller are you using? I tried many controllers on many phones. Using stadia.com chrome desktop view on mobile. It works on 4g but no controller input is detected on any of them on the stadia.com desktop view smartphone accessed website.
Maybe the controller you are using works for me too.
I used both the stadia controller with a USB C to USB C cord and an xbox one controller with bluetooth.
It could be they updated things serverside to fix the controller issues on mobile browsers as PS4 registered some inputs but they were the wrong ones.
@ChubbiesLover did the USB C to USB C cable come with the controller. I'm wondering if I'm missing a cable as I only got a USB A to USB C for the charging brick in the box.
No, you must buy your own c to c cable.