Apple held talks with DuckDuckGo to replace Alphabet's Google as the default search engine for the private mode on Apple's Safari browser, the Bloomberg News reported on Wednesday, citing people familiar with the discussions.
searchengine.party also has the query string links for a multitude of different search engines, as well as a comparison of security tests and privacy policies and other functions
personally though, Tiekoetter has seemed to be more relevant for the “science” tab searches, as it uses Google Scholar which has strong relevance to my searches
I did a quick search and found instructions to what I think you are asking for hopefully this helps. The query string for paulgo.io is “https://paulgo.io/search?q=”
I have also heard Xsearch works
searchengine.party also has the query string links for a multitude of different search engines, as well as a comparison of security tests and privacy policies and other functions
personally though, Tiekoetter has seemed to be more relevant for the “science” tab searches, as it uses Google Scholar which has strong relevance to my searches