Possibly, but even right now when you open Chrome (non-incognito) you immediately get three google analytics cookies set, which are picked up by any website usi

Possibly, but even right now when you open Chrome (non-incognito) you immediately get three google analytics cookies set, which are picked up by any website using google analytics (i.e. almost every website). If you put this together with the fact that Chrome knows about Google Account sessions, you conclude that Google is already keeping track of everything that you, as an individual, does online and has been for many years, even without fingerprinting.