REST API: Introduce controller for searching across post types.

Introduces a `WP_REST_Search_Controller` class which registers a `/wp/v2/search` endpoint. Search types are handled by extending `WP_REST_Search_Handler`. The default search type is `WP_REST_Post_Search_Handler` but can be filtered by plugins or a theme.

Merges [43739,43741] from the 5.0 branch to trunk.

Props danielbachhuber, flixos90, pento, rmccue, joehoyle.
Fixes #39965.


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