Why does a cost show where it came from?

Because a value you typed must never be overwritten by a sync. Every fillable field carries a source: a Shopify prefill, a manual entry, or an import. A sync may fill a field that is still a prefill, and never one you have edited.

It is the rule that makes nouz safe to correct. Shopify catalogues are routinely missing weights and unit costs, you fill the gaps here, and from that moment your value is the one every calculation uses.