As much as I disagree on paying 10$/m for a search engine, I will disagree with your take on their data sharing.

In their privacy policy https://kagi.com/privacy , they state that they collect logs :

• Kagi server identification, configuration, and performance (CPU, RAM, etc.)
• Identifiers that tell us what code paths were taken
• Time measurements of individual steps of request fulfillment
• Summaries of requests made to third parties

Absent from our logs are any identifying information about your client

Tho I'm not sure how they could fulfill these purposes :

• Prevent abuse of our product from bad actors (DDOS, etc.)
• Detecting abuse of our platform

With only logs on how the serice îs used anonymously.

They do send the logs to Sentry for analysis. But without any search query, from what they say.