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/
What I feel is missing from the practical suggestions section: why cache images at all? They should be stored on the server they were uploaded to, and nowhere else. The image URL would be attached to the post, and could then be used by clients to fetch the image from the original server.
I thought lemmy did this, but it seems not (any more?).