Yes your original point was well made. It just wasn’t clear yet how DNS requests would leak search queries. So more precisely, multiple DNS requests with local cache misses in a short period of time can be used to infer search queries. Like if there are DNS requests for google, amazon, and a botany supplier one after another, then it could be inferred that you searched for something related to shopping and plants.
Thanks for the detailed response!
Probably need to look for less than a short. Water is conductive but not THAT conductive.