DuckDuckGo’s policy is much less specific but makes it a point that they aren’t sending your exact IP address to Microsoft or anybody else for any reason. Among other, IMO even better policies.
we share anonymous browser and device information with our hosting and content providers for security and display purposes (for example, that you’re using a mobile device), but we never share any information with them that could tie your searches or website visits to you personally, or that could allow them to create a history of your individual search queries or the sites you browse.