While they don't offer anonymous/private payments, you can use PrivacyPass no matter how you pay for Kagi. So, yes, the fact that you have an account will be known to anyone with access to their subscriber data, but what you search for will not be tied to that identity.

Absolutely not. I don't feel it's necessary to pay the sacrifices needed for a trustless society.

I would much rather be able to have things like personalised searches (which are identifying).