Chromecast says it's corrected to WiFi, I can use Google Assistant to cast things to it, but it doesn't show up in Google home app or allow stadia controller to connect even after 2 factory resets. During set up, everything goes fine until the last step where it says I'm no longer connected to the same network as the Chromecast, even though I literally just used my phone WiFi to allow the Chromecast to join.
I'm guessing that the Chromecast not appearing in the Home app and not wanting to connect with the controller are probably related. I hate to send you away but you might want to check with the kind folks over in the Chromecast Help Community to see if they might be able to help you get squared away:
I'm willing to bet that Stadia will work fine once that's sorted but please do let us know how it goes!