As a matter of fact, Google domains do have (or at least used to have) privileged treatment in Chrome: There are special request headers that Chrome automatically includes in requests to Google-owned domains - and only those. [1]

But even if not, Chrome makes all kinds of API calls to the Google backend, independently of browsing. It would be trivial to e.g. upload the browsing history there and associate it with the user's Google account.

[1] https://www.theregister.com/2020/02/05/google_chrome_id_numb...