From the linked article: "Kagi Translate is free for everyone. If you’re not a logged in Kagi user, you’ll encounter a simple captcha to prevent automated abuse - a small step that helps us maintain quality while keeping the service free. Kagi members get direct access without captchas, integrating seamlessly with their existing workflow."  

 ok, and they also have a GPT-like LLM which seems good and make web searches. 
All free. 
Very suspicious :)