Feature Request: Search Statistics/Analytics (like Kibana)

Before landing on Jetpack Search (for a number of reasons including prices and easy integration), I experimented with a roll-my-own ElasticSearch instance, a couple managed hosts, and a separate service called Algolia.

The primary benefits of those services is that they allow you to see the stats around your searches. You can see what people searched for, what results they got, what the traffic via search is, etc. This allows you to better address the actual needs of your users without guessing.

Features I'm interested in:

* No results - what terms are people searching for that I don't have provided.
* Highest/lowest results - where I should spend more time and money working to improve
* Traffic - Are people actually using my search!?
* Conversation rates - What queries results in hits (or not)

## Examples

* https://www.elastic.co/kibana -- This is part of the default ELK stack, though it tends to be overkill for a lot of people. That would need a simplified, customized, dashboard.
* https://www.algolia.com/products/analytics/?tab=no-results - Their simplified dashboard is probably the best place to start from for WP needs. You won't need to offer the myriad config options, but their analytics are easy to read for the new user and
* https://docs.bonsai.io/article/328-metrics - Bonsai.io is an ES service. Their dashboard shows heat maps as well as an overview ( https://docs.bonsai.io/article/199-cluster-overview ) with how much data you're taking up. So things aren't a mystery.
* https://swiftype.com/documentation/site-search/guides/analytics - Swiftype was bought out by ES I believe, but their basic dashboard is super handy

The issue names no files, tests, or entry points. Start by reviewing the existing Jetpack Search integration and how search requests and results are tracked, then define the analytics scope around no-results terms, result counts, traffic, and conversion rates. Done should include an agreed dashboard design and measurement behavior for the listed metrics.

Written by the indexing model from the issue text.