Can I also use the Google Stadia Controller for games on the PC that have nothing to do with Stadia?
Yes
https://www.pcgameshardware.de/Google-Stadia-Konsolen-269221/News/Stadia-Controller-kabellos-nutzbar-1349558/
Thanks, so could I use the controller to play a game from Steam?
If I've skimmed through the article correctly, this should be possible, yes