If you have spare hardware lying around and a public IP (or a server anyway), you can selfhost SearXNG.
If you’re fine with paying 12$/month (with tax) for a customizable search engine, very accurate and transparently sourced/quoted LLM, and just a better index than any other search engine I know, use Kagi. I heard some rumors and bad things, but nothing to do with privacy, only the aforementioned tax.
And for a free search engine which claims privacy and is an alternative to DDG, with its own index afaik, Brave.