Setting a default value for a Woocommerce product field to all products

I created a custom field for my products using this tutorial, but I need to set a default value for this field.
I have already created hundreds of products and I need to have this field updated at those as well. I’m then using this value to order the products.

Here is the whole code:

// Display Fields
    add_action('woocommerce_product_options_general_product_data', 'woocommerce_product_custom_fields');
    // Save Fields
    add_action('woocommerce_process_product_meta', 'woocommerce_product_custom_fields_save');
    function woocommerce_product_custom_fields()
    {
        global $woocommerce, $post;
        echo '<div class="product_custom_field">';
        // Custom Product Text Field
        woocommerce_wp_text_input(
            array(
                'id' => 'priority',
                'placeholder' => 'Priority of the product - values a>b',
                'label' => __('Priority of the product', 'woocommerce'),
                'desc_tip' => 'true',
                //'default' => '0',
            )
        );
        echo '</div>';
    }

    function woocommerce_product_custom_fields_save($post_id)
    {
        // Custom Product Text Field
        $woocommerce_custom_product_text_field = $_POST['priority'];
        if (!empty($woocommerce_custom_product_text_field))
            update_post_meta($post_id, 'priority', esc_attr($woocommerce_custom_product_text_field));
    }

    function cw_add_postmeta_ordering_args( $args_sort_cw ) {
      $cw_orderby_value = isset( $_GET['orderby'] ) ? wc_clean( $_GET['orderby'] ) :
            apply_filters( 'woocommerce_default_catalog_orderby', get_option( 'woocommerce_default_catalog_orderby' ) );
      switch( $cw_orderby_value ) {
           case 'priority':
                $args_sort_cw['orderby'] = 'meta_value';
                $args_sort_cw['order'] = 'asc';
                $args_sort_cw['meta_key'] = 'priority';
                break;
      }
      return $args_sort_cw;
    }
    add_filter( 'woocommerce_get_catalog_ordering_args', 'cw_add_postmeta_ordering_args' );
    function cw_add_new_postmeta_orderby( $sortby ) {
       $sortby['priority'] = __( 'Recommended', 'woocommerce' );
       return $sortby;
    }
    add_filter( 'woocommerce_default_catalog_orderby_options', 'cw_add_new_postmeta_orderby' );
    add_filter( 'woocommerce_catalog_orderby', 'cw_add_new_postmeta_orderby' );

I could’t find a working solution, so I’m kindly asking you for an advice. What I expect is that every existing product will have this value set and when creating a new one the default value will be displayed. Then it should be sorted according to this value. Thanks for your help!

Edit according to the first answer:
The data does’t update in the database. In the front-end I can only see the products I have manually altered and not those to which the 0 was added using this function. When I try to change the altered value back to 0, it is not updated. Actually I just need a function which would refresh all the products so that the value is stored to the database.