Is it considered impermissible (haram) or permissible (halal) to include the shipping cost in the product price and advertise "free shipping"—with the merchant's website being aware and the total value remaining unchanged?

A merchant is commanded to be truthful in his sales so that his earnings may be blessed and that he may be with the Prophets, the Truthful, and the Martyrs. He must strive for truthfulness and avoid deception, misrepresentation, and lies. Therefore, it is not permissible to write "free shipping" if the shipping cost is added to the total price of the product, as this constitutes lying and deception. Rather, you should say: "The stated price includes the cost of the item and its delivery fee."