Why does my product page show the same SKU no matter which size is picked?

No, the order gets the right code.

The SKU line under the title always shows the product's own code, the one in SKU (parent) in the Inventory card. It doesn't change as the shopper picks options.

When the shopper adds the item to the cart, Wcart uses the SKU of the exact variant they picked, from the SKU column of the Variants card. That's the code saved on the order, shown in the order's SKU column and on the printed invoice.

If the parent code confuses customers, give it something general, for example the style number without a size:

1. Open the product from Products → Products.
2. Edit SKU (parent).
3. Click Save.