There is a Woocommerce web store where inventory management is active, but backordering is allowed everywhere. A code is already set up so that if the inventory falls to 0 or below, the product is added to a special category and marked as sold out but available for order. However, this is displayed only on the simple product page. I would like to achieve that on the store page, it should be visible as a badge whether the product is available or unavailable but orderable. Additionally, since prices are hidden from users who are not logged in using a PHP code, I would like to hide this as well.