You need to use the Google home app to set up the Chromecast. you also need to make sure that the Google account up to the Chromecast is the same one hooked to stadia
I had a similar issue when I was using multiple devices during setup a phone and tablet. In the end I closed the app on all devices. Reopened the app on only the device that I had done the controller synching and this fixed the issue.
For me the specific problem was that when I tried to "add account" via the app the chromecast wasnt showing up. As i said try restarting apps, device, bluetooth etc. If this is your issue as well.
@Counterxap Did you also try these steps to fix the Stadia App? Might be that one of them can fix the issue, otherwise I guess it makes sense to contact Stadia support for this issue.
I dont have the Android App i have the iOS App. Still nothing works when trying to connect the account to the CCU in the App. Loading forever.
I have problems too, i tried it for 3 hours doing everything (with ethernet, without ethernet, with router dual band 2.4/5GHz, with single band 5GHz, ...) I only got it once, and then i tried to use the ethernet cable and then the link code appears and then nothing again (putting off the cable didn't work to get it to work again). I have been restore chromecast sometimes, closing the apps, etc. Even i have use a second wifi network only for chromecast (i have the company's router and a Xiaomi Router as main).
The problem is that the TV shows the message for connect chromecast with stadia app, but neither stadia app or google home can connect to chromecast, it didn't appear in the list of stadia app. I only get it once and the problem i got later was to try to use ethernet...
Tomorrow i will try once and if not i will call Google to get a solution.