"Damascus" barrels are made by winding straps around a mandrel, and hammer "welding" them together.
True Damascus used 6 or 8 straps, and a cheaper version, known as "stub twist" used 2 or 4 straps.
The key visual ID is the barrel has "rings" or lined around it, its entire length.
A Damascus pattern blade is a high grade (expensive) knife. Up until about 100years ago, people thought the same of a Damascus barrel shotgun.
Until smokeless powder came along. While they work ok for black powder, smokeless powder is a different beast, and Damascus barrels ARE NOT SAFE with modern ammo (smokeless powder).
The problem is that while smokeless powder will "unravel" a Damascus barrel, it won't do it in a predictable manner. It may do it on the 1st shot. Or it may do it on the 40th shot, or you may use the gun every season for 20 years without issue and then, out of the blue, a shot goes BLAM and you have steel spaghetti for a barrel.
Look up Damascus barrel shotgun, find a pic, see the lines on the barrel. If your proposed project gun looks anything like that, pass and find another that has a "fluid steel" or "nickel steel" barrel.
Many early barrels moving past damascus were marked "fluid steel" or something similar do differentiate themselves from the older, less sturdy barrels.
"Fluid steel" was the term used by Ithaca (and likely others) for their early solid steel barrels. They are safe for smokeless powder loads (keeping in mind the overall pressure limits of the old guns).
"Nickel steel " was used by Winchester (and others) for their solid steel barrels, and was still marked on barrels made through the 1920s.