Related Posts: add posts to the WP REST API Post Response.

Fixes #3424

To test:
1. Install and activate the WP REST API plugin (v2)
2. Make sure Related Posts are enabled in Jetpack.
3. Visit `http://yoursite.com/wp-json/wp/v2/posts`
4. Look for the new `jetpack-related-posts` field

modules/related-posts/jetpack-related-posts.php

@@ -76,6 +76,9 @@ public function __construct( $blog_id_local, $blog_id_wpcom ) {
 		if ( ! class_exists( 'Jetpack_Media_Summary' ) ) {
 			jetpack_require_lib( 'class.media-summary' );
 		}
+
+		// Add Related Posts to the REST API Post response.
+		add_action( 'rest_api_init',  array( $this, 'rest_register_related_posts' ) );
 	}
 
 	/**
@@ -1282,6 +1285,49 @@ protected function _allow_feature_toggle() {
 		}
 		return $this->_allow_feature_toggle;
 	}
+
+	/**
+	 * ===================================================
+	 * FUNCTIONS EXPOSING RELATED POSTS IN THE WP REST API
+	 * ===================================================
+	 */
+
+	/**
+	 * Add Related Posts to the REST API Post response.
+	 *
+	 * @since 4.0.0
+	 *
+	 * @action rest_api_init
+	 * @uses register_rest_field, self::rest_get_related_posts
+	 * @return null
+	 */
+	public function rest_register_related_posts() {
+		register_rest_field( 'post',
+			'jetpack-related-posts',
+			array(
+				'get_callback' => array( $this, 'rest_get_related_posts' ),
+				'update_callback' => null,
+				'schema'          => null,
+			)
+		);
+	}
+
+	/**
+	 * Build an array of Related Posts.
+	 *
+	 * @since 4.0.0
+	 *
+	 * @param array $object Details of current post.
+	 * @param string $field_name Name of field.
+	 * @param WP_REST_Request $request Current request
+	 *
+	 * @uses self::get_for_post_id
+	 *
+	 * @return array
+	 */
+	public function rest_get_related_posts( $object, $field_name, $request ) {
+		return $this->get_for_post_id( $object['id'], array() );
+	}
 }
 
 class Jetpack_RelatedPosts_Raw extends Jetpack_RelatedPosts {