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<?php
/**
 * The filter is named rest_{post_type}_collection_params. So you need to hook a new filter for each 
 * of the custom post types you need to sort.
 * @link https://www.timrosswebdevelopment.com/wordpress-rest-api-post-order/
 */

// This enables the orderby=menu_order for Posts
add_filter( 'rest_post_collection_params', 'filter_add_rest_orderby_params', 10, 1 );
// And this for a custom post type called 'portfolio'
add_filter( 'rest_portfolio_collection_params', 'filter_add_rest_orderby_params', 10, 1 );

/**
 * Add menu_order to the list of permitted orderby values
 */
function filter_add_rest_orderby_params( $params ) {
	$params['orderby']['enum'][] = 'menu_order';
	return $params;
}