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I surfed through a Google network for a bit a few years ago, and it does reveal things. The most common was Drupal and WordPress sites with some malicious code running that would link to online pharmacies on every page, but only to Google user agents / networks, I assume to boost their ranking. I let a bunch of webmasters know, most of them didn't believe me because they didn't see it themselves.

You wouldn't even need an extension. Both browsers allow you to change your User-agent. An extension just makes it a little easier.

I have a UA switcher on Firefox so I can change my UA in two clicks. One of the built-in UA options is indeed the Googlebot.

Safari has this built in: https://osxdaily.com/2013/01/16/change-user-agent-chrome-saf...

You chose to mention Safari, but link to an article about Chrome, Firefox, and Safari? Looks like all major browsers (probably Edge too) have this built in.

https://github.com/iamadamdev/bypass-paywalls-chrome