https://marginalia-search.com/

Open source and has its own index

Yacy does have its own index it even allows you to crawl the webpages yourself from the settings page problem is that the results you get out of it fucking suck

I really like the concept of yacy just wish the results were better but I think there is value in p2p search indexes yacy is probably the most reasonable search engine to self host since you don’t have to index everything yourself

I have had some success with https://marginalia-search.com/

Which does have its own index it is open source so you could theoretically self host but you would need to make your own index