The search terms are not part of the headers but part of the URL in a GET request. For a POST request those terms are part of the body.

In any event, even before DDG has a chance to encrypt any data Amazon has already logged my search query and IP address.
posted by <hidden> • 4 years and 3 months ago Link

This a common misconception. All headers (including the full URL and search terms embedded in it) are encrypted on a GET request:
posted by yegg Staff4 years and 3 months ago Link