Updating a custom field value without manually saving in a WooCommerce admin product area

Question

I would like to add the normal stock value of a product to the custom stock value that already has an order status (wc-on-hold and wc-processing). This works great, but only when I save the product manually. Is there a way to update the custom meta-field value without this intermediate step?

Here is my Code in functions.php:

// build custom Product fields
function blu_real_stock_status_fields() {
    $domain = 'woocommerce';
    echo '<div style="background:#a1ff7f;" class="options_group">';
    woocommerce_wp_text_input( array(
        'id'                 => '_realer_bestand',
        'label'              => __( 'Realer Bestand', $domain ),
        'placeholder'        => '',
        'description'        => __( 'Die Anzahl aller Produkte, die noch im Lager liegen.', $domain ),
        'desc_tip'           => true,
    'custom_attributes'  => array( 'readonly' => 'readonly' ),
    ));
    woocommerce_wp_text_input( array(
        'id'                 => '_in_bearbeitung',
        'label'              => __( 'In Bearbeitung', $domain ),
        'placeholder'        => '',
        'description'        => __( 'Anzahl der noch nicht versandten Bestellungen.', $domain ),
        'desc_tip'           => true,
        'custom_attributes'  => array( 'readonly' => 'readonly' ),
    ));   
    echo '</div>';
}
add_action( 'woocommerce_product_options_stock_status','blu_real_stock_status_fields', 0, 1 );

 // Get All defined statuses Orders IDs for a defined product ID (or variation ID)
function get_orders_count_for_a_product( $product_id ){
    $orders = wc_get_orders( array(
        'numberposts' => -1,
        'post_type' => 'shop_order',
        'post_status' => array('wc-processing','wc-on-hold')
    ) );
    $count_orders = 0;
    foreach($orders as $order){
        $has_product = false;
        foreach($order->get_items() as $item_values)
            if( $item_values['product_id'] == $product_id )
                $has_product = true;
        if( $has_product )
            $count_orders++;
    }
    return $count_orders;
}

// Get and save Values for custom Product field
function blu_real_stock_status( $product_id ) {
$product = wc_get_product( $product_id );
$number_of_orders = get_orders_count_for_a_product($product_id);
// Output the value

$processing_val = $number_of_orders;

    // Isset
    if ( isset( $_POST['_realer_bestand'] ) ) {
        // ID & value
        $ref_stock_id = '_realer_bestand';
        $ref_stock_val =  $product->get_stock_quantity();
        $ref_stock_val_real = $ref_stock_val + $processing_val;
        
        // Update ref stock
        $product->update_meta_data( $ref_stock_id, $ref_stock_val_real );
    }
     if ( isset( $_POST['_in_bearbeitung'] ) ) {
        // ID & value
        $ref_process_id = '_in_bearbeitung';
        $ref_process_val =  $processing_val;
        
        // Update ref stock
        $product->update_meta_data( $ref_process_id, $ref_process_val );
        $product->save_meta_data();
    }
}
add_action( 'woocommerce_admin_process_product_object','blu_real_stock_status', 0, 1 );