The site is not making any requests if you click the button (which is just a div by the way). Client-side it writes this entry in your local storage and that’s it:
googledevai-gemini-voted-project-list: ["your-project"] // list of projects you already "voted" for.
Delete that (or refresh in incognito mode) and it’s gone and you can “vote” again. You can also “vote” in offline mode…
A statement from Google would be nice. Please, please enlighten me how this works because it would be a shame if it just didn’t.