From a practical standpoint exactly what does Google collect from one’s browsing activity when they use Chrome? Not sure I’ve ever seen the technical analysis of what kinds of exposure users have.
I'm sure it's not limited to this but there are a lot of dark UI patterns in Chrome, e.g. any Google web login also logs you in to Chrome so Google "has permission" to record your browsing history and other browsing data.
After the blowback from auto sign-in they added an option to disable that on both Chrome and ChromeOS.
Settings -> Advanced -> Allow Chrome Sign-in
If you want even more control use ADMX (enterprise policies) to permanently disable it. For example on Windows visit Software\Policies\Google\Chrome\ in either HKLM or HKCU and set SyncDisabled 1, EnableSyncConsent 0, BrowserSignin 0.
I mean, I think Google gathers browsing history through other means (being embedded on a huge proportion of all webpages), but in the case of Chrome/Chromium, there is a separate password for the sync artifacts, I think at least in principle they are stored separately (especially since they now include passwords, social security numbers, etc.).
My sync password is different from my account password, I think it generally unlocks both at once if your sync password is the same as your account password, and you log in to your Google account.
I think this is also possible with the way that Microsoft has made "Edge" work with Microsoft accounts rather than Google accounts.
Nowadays your Chrome Sync/Backup is encrypted with your G password (and you can change it to a separate password if you wish), but a lot is still sent to Google (and IIRC by default): https://support.google.com/chrome/answer/9116376?hl=en ("Learn about other Google Services")