Oh, okay, I didn't realize that you were trying to just ask people here about their search engine, rather than link to an article about Orion.

Well, I use Kagi's search engine. They basically do what I wish Google and YouTube and suchlike would do

just make their money by charging a fee and providing a service, rather than trying to harvest data and show ads. I use search more than any other service online, and there isn't really a realistic way for me to run my own Web-spanning search engine and getting reasonable, private results. I don't really make use of most of their add-on features other than their "Fediverse Forums" thing that can search all Threadiverse hosts, which is helpful, and occasionally their Usenet search functionality. My principal interest in them is from a privacy standpoint, and I'm happy with them on that front; they don't log or data-mine.

EDIT: They do have some sort of way to issue searches without telling Kagi which user at Kagi you are, if you're worried about them secretly retaining your search results anyway, which I think is technically interesting, but I really don't care that much. If a wide range of websites adopted the system, that'd be interesting, maybe.

EDIT2: Privacy Pass. Might be the protocol of the same name that CloudFlare uses. I've never really dug into it.

EDIT3: Some of their functionality (user-customizable search bangs, for example) can also be done browser-side, if your browser supports it and you rig it up that way. Like, I had Firefox set up to make "!gm <query>" do a Google Maps search before Kagi did, and chuckled when I realized that they defaulted to the same convention that I had.

EDIT4: Oh, their images search does let you view a proxied view of the image (so that the site with the result doesn't know that you're viewing the image) and lets one save the image. IIRC, Google Images used to do something like that, though I don't believe they do now, so places like pinterest that try to make saving an image a pain are obnoxious. Firefox on the desktop still lets one save any image visible on a webpage (click the lock icon in the URL bar, click "Connection Secure", click "More Information", click "Media", and then scroll through the list until you find the image in question), but I'd just as soon not jump through the hoops, and Kagi just eliminates the whole headache.

EDIT5: They try to identify and flag paywalled sites in their results, unlike Google. For example, if you kagi for "the economist American policy is splitting, state by state, into two blocs", you'll get a result with a little dollar sign icon. This can be helpful, though archive.today will let one effectively bypass many paywalls, which somewhat reduces the obnoxiousness of getting paywalled results just mixed in with non-paywalled results on Google.

Your title still says "Kagy" instead of "Kagi".