Seconding, Kagi is great. I hope they succeed…

This is an absolutely valid concern. The answer here, unfortunate as it is, is trust. There's probably things they can do here to remove the need for an actual identity (Mullvad's payment model comes to mind), but I suspect that takes more legal/financial infrastructure than they have access to at the moment.

PS: I am not a lawyer, but for what it's worth, if you _pay_ for Kagi and they advertise their privacy policy as a feature you pay for (see https://kagi.com/privacy), one could reasonable sue for false advertising or demand a refund for not providing a promised service. This would make any pushback subject to consumer protection laws in addition to whatever nascent privacy law they may be subject to.

There's not much to understand about it, you just have to take their word for it that they're not storing anything. There's no way for the clients to enforce that, and I can't figure out any model that they could use to have a paid search engine that can guarantee privacy with zero trust. (Edit: a sibling points out Mullvad's payment model would help towards guaranteeing pseudonymity)

I pay for Kagi less as a privacy thing and more because it's a better search engine and consistently gets me better results than Google does.