How to Add “Random” option on Product List Widget

Hi,

I need to show the products (featured/on sale/latest) in random order. By default it only has ASC or DESC options only. How can I add an option to choose Random for this widget?

I checked the page https://woo.com/document/woocommerce-widgets/ but no clue.

for the shop page, I was able to add the random option with this code

// Add "Random Products" option for shop page (Apperance > Customize > WooCommerce)
add_filter( 'woocommerce_get_catalog_ordering_args', 'custom_woo_catalog_ordering_args' );
  
function custom_woo_catalog_ordering_args( $args ) {
$orderby_value = isset( $_GET['orderby'] ) ? woocommerce_clean( $_GET['orderby'] ) : apply_filters( 'woocommerce_default_catalog_orderby', get_option( 'woocommerce_default_catalog_orderby' ) );
  
if ( 'random_list' == $orderby_value ) {
$args['orderby'] = 'rand';
$args['order'] = '';
$args['meta_key'] = '';
}
return $args;
}

add_filter( 'woocommerce_default_catalog_orderby_options', 'woocommerce_catalog_random_orderby' );
add_filter( 'woocommerce_catalog_orderby', 'woocommerce_catalog_random_orderby' );

  
function woocommerce_catalog_random_orderby( $sortby ) {
$sortby['random_list'] = 'Random';
return $sortby;
}

How can add the similar option on Product list Widget?

Thanks!