Kagi's privacy guarantee is more of a "trust me bro" and I say that as a Kagi subscriber. While they may claim that they preserve privacy or anonimity as long as it's tied to a user account, or payment information nothing prevents them from associating searches with user. Even protonmail enabled logging for a particular user at one point. Their guarantee is on the same level.

At the same time, privacy pass is a very foreign concept to me. If they are transferable between devices, one could generate a couple and resell them over some other medium (even in person).