I can't recommend a self hosted SearXNG instance enough.
DDG uses Bing as a search backend last I checked, and the founder/CEO is spoke in favour of censoring search results that don't match with his worldview.
searx and searxng are not search engines, and searx is more private (searxng collects info from users, which searx never wanted to). AFAIK duckduckgo is neither a search engine on its own, it uses blink...
To tell the truth, only yacy and sightnet have own index(database).
Others are meta-search engines. They work like proxy. It's called meta search. (https://en.wikipedia.org/wiki/Metasearch_engine)