register_post_status example

            'rest_base'             => 'navigation',
            'rest_controller_class' => 'WP_REST_Posts_Controller',
            'supports'              => array(
                'title',
                'editor',
                'revisions',
            ),
        )
    );

    register_post_status(
        'publish',
        array(
            'label'       => _x( 'Published', 'post status' ),
            'public'      => true,
            '_builtin'    => true, /* internal use only. */
            /* translators: %s: Number of published posts. */
            'label_count' => _n_noop(
                'Published <span class="count">(%s)</span>',
                'Published <span class="count">(%s)</span>'
            ),
        )
    );