I know this is an old image, but
I believe that without logging in with your account, the services you use from google are:
- search bar autocompletion / search suggestions (can be turned off)
- default search engine (can be changed)
- URL checker for malware and the likes
- URL errors (I think it performs a google search , offers you a cached version etc)
That's it. Not sure if chromium uses any of these.
Other things such as saving your history, your searches, etc... only happen if you're logged in with your google account (in chrome, I doubt chromium even has this).