DuckDuckGo had some partnerships with at least Yahoo in the past but I'm quite certain they now run their own crawlers and build their own search index. Brave Search is another really promising privacy oriented web search with an AI chatbot that they claim run on.
I don’t see how X could achieve anything better than what is already on the market just by scraping search results from other search engines. They must run their own web spiders and with the AI know-how they have they should be better equipped for running a search engine than the other web search providers were 10 years ago.
RE: Elon Musk declares war on Google