This is from DuckDuckGo's privacy policy: "We don’t track you. That’s our Privacy Policy in a nutshell. We don’t save or share your search or browsing history when you search on DuckDuckGo or use our apps and extensions."
If the court compelled DuckDuckGo to log all searches, I would be equally concerned.
OpenAI (and other services) log and preserve your interactions, in order to either improve their service or to provide features to you (e.g., your chat history, personalized answers, etc., from OpenAI). If a court says "preserve all your user interaction logs," they exist and need to be preserved.
DDG explicitly does not track you or retain any data about your usage. If a court says "preserve all your users interaction logs," there is nothing to be preserved.
It is a very different thing - and a much higher bar - for a court to say "write code to begin logging user interaction data and then preserve those logs."
It would be interesting to know how much Microsoft logs or tracks.