> (..) since Firefox shares same "Safe Browsing" database with Google

This. Firefox even sends the hash and filename of each download to Google. So if you use Firefox to download the Tor browser, an abortion price list or a secret PDF, Google knows you downloaded it.

https://www.pentagrid.ch/en/blog/block_browser_requests_to_g...

Disclaimer: The blogpost is two years old, but I assume this is still current.