How to display a list of all published products variations IDs on Woocommerce

My goal at the end is adding all my variations to the cart fast using only the ID list of the variations, but whatever I try I can't get to display a list of this variations on the cart page...

add_action( 'woocommerce_before_cart', 'custom_echo_product_ids' );

function custom_echo_product_ids() {

   $all_ids = get_posts( array(
        'post_type' => 'product',
        'numberposts' => -1,
        'post_status' => 'publish',
        'fields' => 'ids',
   ) );

   foreach ( $all_ids as $id ) {
        echo $id->get_children() . , . ;
   }
}