The 10 or so Damascus guns I own haven't noticed if I shoot BP or nitro in them. Been doing it for around 15 years and 95% of the time with nitro.
Congratulations, you haven't had a problem...YET...
You may never have a problem, I hope you don't.
Or you might have a barrel let go the very next time you pull the trigger. there's no way to know, and that's the problem.
"True" Damascus barrels used 6 or 8 straps, wound around a mandrel and hammer welded into a barrel. Twist (or Stub Twist) barrels were made the same way, but used only 2 or 4 straps.
Damascus barrels were made during the early part of the smokeless era, for a couple reasons, first, was that they had been, and still were in demand by the comsumers, Damascus barrels were seen as a sign of high quality, and kept that reputation for some time, despite the superiority of "fluid steel" or "Nickel Steel" barrels. Over time, that changed, Damascus production ended (in the US at least) leaving the modern solid barrel the dominant type.
Second reason, was simply that even after smokeless "took over", a lot of people still used black powder reloading their shells. Over time, the "bulk" smokeless powders (such as DuPont's PB) replaced black, and then eventually more modern smokeless became the standard.
My Grandfather had a "stub twist" Ithace he was very fond of. Soo was one of his neighbors, who badgered him for about a decade before Grandpa gave in and sold him the gun. The gun my Grandfather replaced that gun with is the one I currently have, which he bought new in 1909. It has "fluid steel" barrels.
His old stub twist gun gave good service for several more decades, then 8 inches of the left barrel unraveled in the 1940s. Might have been smokeless ammo, we don't know, and of course no way to know, now.
Point here is that Damascus barrel guns are a potential problem, there's no way to tell if there is rust or bad welds in the voids produced by the hammer welding method that weakens them, until the barrel lets go. IF it does.
In some ways its like the "low number Springfields" that "shouldn't be shot" today. People have been and probably still are shooting some of them with no problems. Others have had catastrophic failures.
Since it is possible (but not a given) people advise not to shoot them at all.