WooCommerce custom product type not saving with namespaces

I am try to create my custom product type, but when I save it is still simple product. This because I am using namespacees but I can not figure out the problem.

This is class with new pt

namespace giftbox\models\woocommerce;

class WC_Product_Giftbox extends \WC_Product_Simple
{
    protected $product_type = 'giftbox';

    public function get_type()
    {
        return 'giftbox';
    }
    
}

the name of the class I think is correct and I understood I don't need construct in WC 3.0

Then I have the class extend WC_Product_Giftbox

namespace giftbox\models\woocommerce;

class product_type extends WC_Product_Giftbox
{
    /**
     * Build the instance
     */
    public function __construct()
    {

        add_filter('product_type_selector', array($this, 'add_type'));
        register_activation_hook(__FILE__, array($this, 'install'));
        add_filter('woocommerce_product_class', array($this, 'new_woocommerce_product_class'), 10, 2);
        ...
    }

    
    /**
     * Giftbox Type
     *
     * @param array $types
     * @return void
     */
    public function add_type($types)
    {
        $types['giftbox'] = __('Gift Box', 'giftbox');
        return $types;
    }

    public function install()
    {
        // If there is no giftbox product type taxonomy, add it.
        if (!get_term_by('slug', 'giftbox', 'product_type')) {
            wp_insert_term('giftbox', 'product_type');
        }
    }
   
    public function new_woocommerce_product_class($classname, $product_type)
    {
        if ($product_type == 'giftbox') {
            $classname = 'giftbox';
        }
        return $classname;
    }


}

Then in controller I just call the class

new product_type();

The new product type is there and is possible to select it, but if I try to save or update continues to remain simple product.

I check it inside database and is missing my custom product type but I am not sure if have to be saved there or not.