I am familiar with the mechanics of Privacy Pass. Both using privacy pass and publishing the source code of their implementation does inspire confidence towards their claims of search anonymity. Verifiability of the VOPRF is essential here, otherwise I would posit the deployment could be built from something other than the source code.

However, I always apply a couple layers of (probably too much) skepticism when dealing with any entity incorporated or doing business in any five eyes country.

Is there verification that Kagi doesn't do any side channel fingerprinting of the client? If so, I would actually consider paying for Kagi if the price was right. SearXNG has been becoming much less effective since the surge of AI scrapers caused everything on the web to lock down APIs.