/**
* Register post meta data in REST
* Use rest_api_init to register post's meta data
*/
add_action( 'rest_api_init', 'add_post_meta_to_rest' );

function add_post_meta_to_rest() {

    $post_type = 'post'; // You can use taxonomy or a custom post name.
    $rest_name = 'post-meta' // All meta fields will be stored under this REST attribute.

    register_rest_field( $post_type, $rest_name, array(
        'get_callback' => function ( $object ) { return get_post_meta( $object['id'] ); },
        'schema' => null,
        )
    );
}