Which search engine doesn't call any
APIs and has great privacy?
This question seems strange to me and makes me think you don't know the difference between API calls on the backend and sending http requests from the users browser?Go to https://duckduckgo.com/ and open your network tab. You will never see any requests to non-DDG owned websites.
Your site sends requests to all kind of companies. Which exposes data about your users (IP, UserAgent, that they use you.com ...) to those companies.
Maybe you should talk to your devs about it.