Brave and DuckDuckGo mostly use Bing's index. I think DDG use to buy data from Yandex back in the day, but I'm not sure if they do anymore. The only major crawl indexes are Google, Bing and Yandex now. Yahoo and others got out of the game a long time ago.
There is Kagi, a paid search engine (that has a free trial) but I didn't find it all that much better honestly.
You can also try running a local Yacy node (distributed search engine) and set it up to crawl your favourite sites, but it's still pretty buggy.
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