However, there are independent engines out there. The first one that pops to mind is Gigablast, which does it’s own indexing/crawling.

Gigablast went down 2 months ago. The crawler is available as free software, though.

Mojeek’s Search Engine Map gives you a good picture of the search engines out there. You can also see Seirdy’s very informative post on all the different search engines out there, which is fairly regularly updated: https://seirdy.one/posts/2021/03/10/search-engines-with-own-indexes/