REST API: Use new `rest_get_route_for_post()` in the post search handler.

In [48273] the rest_get_route_for_post function was introduced. This simplifies determining the REST API route for any given post object and adds a filter for custom controllers.

Props ravatparmar.
Fixes #50529.

Built from https://develop.svn.wordpress.org/trunk@48381


git-svn-id: https://core.svn.wordpress.org/trunk@48150 1a063a9b-81f0-0310-95a4-ce76da25c4cd