Hi,
I edited the view "order | invoice" and "order | address_template" in order to make it work properly.
The view "order | invoice" had already an override for your website so it did not use the function:
$class = hikashop_get('class.address');
echo $class->displayAddress($this->element->fields,$this->element->billing_address,'order');
to display the address.
The old "invoice" view you were using loaded the address template without an address as parameter.
So the address template could not know that the address had a VAT.
With the code from HikaShop 2.3.4 ; it is working fine.
The invoice and shipping invoice are correct in the backend.
Regards,