Yes, I'm aware of @gemini on Chrome. If you look at how it's implemented they are purposely stashing the query into a HTTP header so it's not possible to use a simple bookmark to launch it.
Query parameters are so tired. All my homies embed their queries into the password portion of a basic auth header. Keeps your queries super secure from spies and competing browsers.
https://imgur.com/a/qxap6iI
Setup the way I have in the image you can simply type @claude and your search
Worth noting that Gemini also offers a URL shortcut for searching Gemini via @gemini within the Chrome browser.