We actually did complete the work of logging the information. You can try out:
SELECT term, count(*) searches,
sum(case when clicked_topic_id is not null then 1 else 0 end)
"continued from search"
from search_logs
where created_at > current_timestamp - interval '30' day
group by term
order by count(*) desc
limit 100
It Data Explorer, it will show you top 100 searches and even counts of who actually clicked through from search. I find the results super interesting.
We will work on exposing some more of this via the dashboard direct.