@sam have you ever considered using Google Analytics events?
I realized I am able to see a number of URLs with query parameter in google analytics. I guess this is triggered either on mobile or when users hit enter. Of the 1000 searches being shown, the large majority seem to be searches for category names. And often when restricted to the topic level (context=topic), the queries are returning 0 results.
If I’m not mistaken, on mobile it is default to search within the topic, but on desktop, the option was default unchecked. Not sure if this inconsistency was intentional.