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