You're not going to have much luck finding a search engine with good results that doesn't depend on google or bing. Kagi is no different. Using a searx instance is probably best if you're looking for something without official agreements with bing or google. Edit: Here is a list of independent search indexes I just discovered in another thread https://seirdy.one/posts/2021/03/10/search-engines-with-own-indexes/
You're not going to have much luck finding a search engine with good results that doesn't depend on google or bing. Kagi is no different. Using a searx instance is probably best if you're looking for something without official agreements with bing or google. Edit: Here is a list of independent search indexes I just discovered in another thread https://seirdy.one/posts/2021/03/10/search-engines-with-own-indexes/