Although the average user might understand that “websites you visit might still track you”, I’m not sure they realise that a lot of websites secretly have a google tracking token which then records their cross-site activity and links it back to their google account if they login.

IMO there is a difference between “the websites you visit might track you” and “the websites you visit might have a google tracker on which will mean we will still track your activity and the sites you visit with that token and link them against your identity”. The first might be technically true, but I think a lot of users would be surprised by the second more nuanced version.