My brother got me a $60 Google Play gift card specifically for buying Stadia games and it doesn't show up as an option in the Stadia Store.
@Tlinzi Paying with Google Play balance only seems to be an option in the Stadia phone app, not in the Chrome version.
And it may even be Android-only - I don't have an iPhone so I can't confirm that.
I'm trying on Iphone and it does not seem to be an option.