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.

Self hosted SearXNG still passes your queries to big search engines so there's still a bit of data correlation they can do, but not nearly as much compared to you visiting their site and getting tracking cookies and all the rest. You can also set up additional proxies to reduce even that exposure further.

It's just not the best self hosted app. I have an instance on my Raspberry Pi which is really slow and I often have to hit search twice to get results. It often gives me results that have a tenth-page-of-google feel. I tried running an instance on my more powerful desktop but the search engine integration doesn't work so I have to open the searx landing page and then search. You can add more upstream search engines as well, but in doing so I've broken all possibility of getting pertinent results.

I use a public instance at work as well but I often find myself going to google or ddg anyway as only a handful of results on searx are relevant.

Tdlr: it's a cool idea, but a bit immature.

Comrade Dessalines seems to like startpage https://github.com/dessalines/essays/blob/master/favorite_apps_and_services.md