Jetpack Search: support search queries in backend (WP Admin)

Currently, we only support search queries in the front-end. We expect that Jetpack Search can work in the backend (WP Admin) as well.

From 2265657-zen:

> Would be great to replace the entire search, not only for post search but for tags and images in the media library, these are the three heaviest task in high traffic sites, Elasticsearch can really help here.

From our Jetpack Search lead @gibrown:

> it is something we want to do, but won’t happen this year.

Start by reviewing how Jetpack Search currently handles front-end queries and how WordPress exposes search in WP Admin. Clarify whether the scope includes post search, tag search, and Media Library image search, then define completion as Jetpack Search supporting the agreed backend surfaces.

Written by the indexing model from the issue text.