Barrels are manufactured by boring a larger diameter bar with a "gun drill" which is a single sided cutting tip to make it cut a long straight hole (believe it or not). The bore is then reamed and and honed to finish diameter.
I have to disagree with you here Chuck. You are assuming a single manufacturing process was used in all places at all times. We both know this is not the case.
Longitudinally welded barrels were very commonly used. At first this was a hand process. Later a mechanized process was used.
It is also not the case for damascus barrels. They were all created using a mandrel. At least in western Europe. The chemise was predominately Belgian, but not singular to them.
Pete