Google Stadia is now available via a browser-based interface available to iPhone and iPad users on Stadia's website. The cloud gaming service has long been unavailable to Apple users due to restrictive policies.
Google's workaround was to create a web-based version of Stadia that can be run through the Safari web browser and is now available in a public beta. If you want to try it out, you can play many popular game titles, like NBA 2K21, DOOM Eternal, Red Dead Redemption 2, Assassin's Creed Valhalla, and more.
Google states that the Safari gameplay experience is still under development, and additional features, enhancements, and performance improvements are to be added going forward as it gathers user experience data. The Stadia experience on iOS will probably be similar to Stadia on Android, also the web app supports not only playing but purchasing games as well.
You can start playing Stadia which can be added to the Home screen and launched like a traditional app by going to the Stadia website, tapping on the share button, and picking the add home screen button.
Google Stadia is obvious not a traditional app available to download via Apple's app store, however, this workaround via the Safari web browser should do the trick.