> I've always done my best to search from a browser context that isn't logged in as a result.
It isn't sufficient to avoid being logged in — you have to ensure that the search strings alone, grouped by IP address or some other signal, aren't enough to identify you. When AOL publicly released an archive with 20 million search strings in 2006, many users got exposed:
https://en.wikipedia.org/wiki/AOL_search_log_release
There's also the issue of a site's Terms of Service when not logged in, which may allow an AI to be trained on your interactions — which could potentially bleed compromising information into the generative results other people see.