They say they store all your searches in their privacy policy (but "not in a personally identifiable way" they claim). They also say they effectively rewrite your search results to insert affiliate tracking.

Even if their entire stack was opensource and you had strong visibility and guarantees regarding the code they're actually running in production, adversaries could be exploiting DuckDuckGo and recording all the information you send to them "in a personally identifiable way". So, basically, don't trust DuckDuckGo. They're yet another for-profit middleman (maybe parasitic, maybe not, we don't know) that, through its centralized information accumulation, enables the sort of behavior you claim you want to avoid.