Stadia Enhanced solves what, to me, is the most obvious problem on desktop:
there's no way to search for a specific game in the Stadia store.
How Google, a search company, has neglected to put a search bar on the Stadia Store website for this long is beyond me, but this extension remedies that by putting it right at the top of the page
https://chrome.google.com/webstore/detail/stadia-enhanced/ldeakaihfnkjmelifgmbmjlphdfncbfg
Stadia Enhanced is completely free to use, and it's also open source.
project's GitHub page.
https://github.com/ChristopherKlay/StadiaEnhanced