isnt that the point of neocities?

I found some sites with this concept:

https://wiby.me/

https://www.oldavista.com/

https://sloop.nz/

https://marginalia-search.com/

RIP Frogfind

Yahoo uses the bing index, and aside from Google, Bing, and Yandex the only other larger english general search engine with its own index is Mojeek. Seirdy's blog has more info on this along with reviews of more niche engines, and there is also the search engine map if you want something more visual.

pretty much. DDG for example uses a bing-yahoo "alliance thing" (can't remember what it's officially called but Microsoft and Yahoo have a sort of partnership in this regard).

Your options for actual first party search options are literally pretty much the ones you listed. Yandex is russian so not trusting those guys anymore than I trust Google or Microsoft so that just leaves Yahoo which is...yeah.

Honestly people are just better off using something like SearX or 4Get. they're all the same except with those two you're not going to get the AI slop or ads.

Kagi has its own search engine and internal web indexing:

https://help.kagi.com/kagi/search-details/search-sources.html#search-sources

There's a UK search engine called Mojeek that has its own index. I won't claim it's results are as good as Google/Bing/Kagi etc but if you want to use an alternative it exists. I typically start all my searches there and then transition to DDG if I can't find what I'm looking for.

There are no Chinese search engines?