Log search queries in Analytics

[tomodwyer]

So that we can figure out where gaps in our documentation is.

Things to consider:

1. Should we log all requests, or a sample of requests?
2. Should we log when input is paused, or only when a result is clicked on?
   1. What if they don't find what they are looking for?
   2. Do we also check when the input focus is removed?
3. Do we need to update the privacy policy to reflect this change?
   1. Do we need to consider how to redact data?