Hey @CaptainG,
unfortunately people don't tell you when selling the Stadia controller what else you need to be able to play Stadia.
You can find the requirements though in this article.
At the moment to be able to play you need a Stadia Founder's Edition, Premiere Edition, or a Stadia Buddy Pass.
You could also wait until Stadia Base is out, then you are able to play Stadia with your controller without needing to buy a Premiere edition. For the TV you need a Chromecast Ultra though, but those you can also buy separetely then.
@CaptainG : Yeah, you'll just have to wait for the base edition to be released if you don't want to spend some additional money on a Premium edition release, or obtain a buddy pass code.
I know you feel stung on this currently, but the information is out there if you had searched in the right places. It is what it is currently, and I don't think that Google have intentionally gone out of their way to cause you hardship, but I agree it's far from ideal for users that thought purchasing a controller was sufficient.