Kagi is privately owned US corporation.
> And how do we know Kagi doesn't end up the same way as DDG?
Being a paid service means Kagi's incentives are very different. Instead of selling your data or profiting from feeding into ad-tech food chain, we are interested in selling you a subscription. This changes everything as the number one thing in Kagi's universe becomes what the users want, different to DDG, Google and other ad-supported search engines.
> How do we know these privacy claims are true?
Sadly I can not think of a way to verify them (let me know if you have one). But most plainly, we have no incentive or reason to do otherwise. Note that the only private information Kagi asks of the user is an email address, need to create an account, and those concerned can use whatever email they want.
> But most plainly, we have no incentive or reason to do otherwise.
One reason is: to improve your services. Other reasons could appear over time.
> Sadly I can not think of a way to verify them (let me know if you have one).
The privacy claims could be verified by recurring external audits.
Not in reality. Nothing prevents a bad player from misusing user data once an audit is done. External audit would only be a good cover.