I never had a single “website blocked” dialog because of safe browsing. Meanwhile UBlock Origin often blocks websites, fullscreen with a warning.
On Firefox Safe Browsing is proxied through their servers and anonymized, so I use it. But tbh I have no idea how useful that is?
I use Search Engines (DDG, Startpage, SearX) or Bookmarks and never had such a block, does it directly filter those sites from search results?
The warning screen is a privileged page in Chrome and Firefox. Extensions cannot tamper with it.
More likely you simply haven’t been on a page confirmed by the browsers to be phishing or malware. As you said, you mainly go from search engine results, which do their own cleanup