Search: use our API to replace the results from core JSON API post search

See the `search` arg for https://developer.wordpress.org/rest-api/reference/posts/#arguments

I don't think this yet works, and especially doesn't with instant search. We should:
- verify that our search api can power the core json api for post search
- add some settings or filters for controlling it
- advertise that this works

The issue points to the WordPress posts REST API search argument, Jetpack’s search API, and instant search, but names no files or tests. Start by verifying whether the search API can power core JSON API post searches, then determine the needed controls and public guidance; done means the supported behavior, settings or filters, and documentation are agreed and validated.

Written by the indexing model from the issue text.