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.
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danielbachhuber