Earlier quoted context omitted.
Kagi already provides a way to search anonymously via a random email address (we do not really verify it or need it for anything) and Bitcoin/Lightning payment [1]. Since you are interested in cryptography, there is a discussion on Kagi feedback site along the same lines as your idea, about possible ways to achieve this without the need for cryptocurrency. [2] [1] https://blog.kagi.com/accepting-paypal-bitcoin [2] ht…
Thanks for the links. Using a disposable email with crypto payments and occasionally generating a new account to unlink from previous searches could be a viable intermediate solution. Also, I found this link [1] in the thread you mentioned. They seem to have implemented something like that. [1] https://metager.de/keys/help/anonymous-token
However there is no technical way of proving it. So cryptocurrency and cryptography are ways to achieve anonimity from a perspective of a user, regardless of what we are doing.