Search: not storing debug bar info for es-admin queries

Found this bug by code inspection, so not positive on the steps to reproduce. See p3QzjZ-W8

#### Steps to reproduce the issue

1. Install es-admin from https://github.com/alleyinteractive/es-admin/
2. Install Debug Bar and enable
3. Run a search query on posts in the admin
4. See that the ES query is not shown in debug bar

#### What I expected
We should be able to debug search queries from the debug bar

- es-admin is calling jp search correctly I think: https://github.com/alleyinteractive/es-admin/blob/master/lib/adapters/class-jetpack-search.php#L126
- jetpack is not storing searches when in the admin: https://github.com/Automattic/jetpack/blob/master/modules/search/class.jetpack-search.php#L178

Start with modules/search/class.jetpack-search.php at the referenced line and compare its behavior with es-admin's lib/adapters/class-jetpack-search.php line 126. Reproduce the admin search using es-admin and Debug Bar, then verify that the resulting Elasticsearch query is shown in Debug Bar.

Written by the indexing model from the issue text.