SearXNG is not a search engine. It is a Meta Search Engine. It is self hostable so you can choose any instance that you trust or host it on your own. It compiles and shows you results from other search engine. This way, when you use an instance of SearXNG, your IP address and other metadata is not leaked to any other platform.

I’m never sure about what privacy actually constitutes anymore. But since you can just run your own instance of SearX, I would guess yes. You should have control of everything you look up in the internet. Though sites you enter can still log info they get from you anyways, that can only change through other methods. I tried running my own instance of SearX for a while with moderate success, but it is something that requires more knowledge and time than I have, so I just reverted to use Brave Search. It was decent enough, I guess, but I feel that something, I don’t know what, was always lacking from it. I also was never able to run it in a reliable way for some reason, probably my fault. If you don’t host your own but rather use someone else’s instance, then you just have to trust said person/org I suppose.