The AI is pretty benign, too. They offer diverse models and they make it as privacy-preserving as possible, considering you can opt to use closed models. They are very open about training and retention: https://help.kagi.com/kagi/ai/llms-privacy.html. An interesting note there on models served by OpenAI: "The Assistant does not include a unique user identifier for these requests." I don't know if you can trust OpenAI, but Kagi is at least doing its part.

Also, All the AI integration into the product is gated by a single setting.