yes, it's only a separate widget at the moment, which doesn't really make much sense since such code can be inserted manually, but will there be an option in the component settings to have the "Automatic sign-in" button appear on the Joomla registration page?
and will there be the same option for the SCLogin module, which would show the "Automatic sign-in" button instead of the current static Google logo?
I've seen similar things implemented on many websites - they no longer use a static "register/login via Google" button, they use this form with automatic display of your Login account.
I think you can see something like this when you try to log in to Twitter or Reddit (if you have previously logged in to the same browser using your Google account)