Very strange to put Kagi as “less private” when it’s the only non-self-hosted option that allows for completely private searches with their Privacy Pass tokens. You can access them with Tor, pay with crypto (not really that private though), and sign up with a fake email. kagi.com/privacy#anonymity
Kagi Search Privacy
Better search results with no ads. Welcome to Kagi (pronounced kah-gee), a paid search engine that gives power back to the user.
It isn’t marked as less private. It is grayed out because it is not based in Europe. I personally use them as I find them the best option with what is out there.
The text at the bottom says “kagi doesn’t collect any identifying data, but does require an account, so it is considered less private than the alternatives”.
With fingerprinting and even just IP tracking, I think the question is more whether they can be trusted to not track you (i.e. whether it makes business sense).
But they allow access over Tor and their privacy tokens means they can’t tie your search to your account, so they both don’t get fingerprinting nor know who is even making the request.