Actually, it looks like it's not websites that see Google login status, but the browser itself. I say this because there was one time by chance that the login popup stayed visible for a moment when I entering the tab menu, meaning the popup must be a part of the browser UI and not in the webpage. The popup also stays the same size when zooming in/out of a page, and its text cannot be highlighted like other text on a page.
So it may very well be that websites aren't seeing Google cookie/login status after all, and Vanadium/Chrome happens to have a feature to detect a Google login session (which it has every right to do) & to offer a Google login on sites that support it. If that's the case, there'd be no 3rd-party cookie/session sharing involved, and I'd be satisfied :)