As others have stated, you are mixing search engines with metasearch engines here. If you employ browser isolation and obscure your IP address, you can be anonymous with any engine.

Yacy has potential, and I run an instance. It relies on us operators to index sites. You will find results to be incomplete in many areas, but it can be great for researching controversial topics. When I want uncensored and not manipulated results, I also use Yandex.com and Brave.