The first smokeless powder for shotgun shells was Wood powder introduced in 1876. Shotgunners being a hidebound lot were rather slow to embrace smokeless powder, but by the 1890s it was coming on strong. In 1890, Captain A.W. Money came to America from England, and established the American E.C. and Schultze Powder Company in Oakland Park, Bergen County, New Jersey, with offices on Broadway in New York City, to manufacture smokeless shotgun powders. In 1893, Union Metallic Cartridge Co. was already offering smokeless powder shotshells, and that year Winchester was providing them to selected shooters with Winchester offering them to the general public in 1894. The American ammunition companies held their smokeless powder loads offered in the 2 5/8 inch 12-gauge shells lower than those offered in the 2 3/4 inch and longer shells. The very heaviest 2 5/8 inch shells I find offered were 3 1/4 drams of bulk smokeless powder or 26 grains of dense smokeless powders such as Ballistite or Infallible with 1 1/4 ounces of shot. In 2 3/4 inch and longer shells they offered 3 1/2 drams of bulk smokeless powders or 28 grains of Ballistite or Infallible dense smokeless powders with the same 1 1/4 ounce of shot. These loads were very high pressure according to a DuPont Smokeless Shotgun Powders (1933) book I have. It shows the 3 1/2 drams of DuPont bulk smokeless powder pushing 1 1/4 ounces of shot as being 11,700 pounds; 3 1/2 drams of Schultze bulk smokeless powders pushing 1 1/4 ounces of shot being 11,800 pounds and the 28-grains of Ballistite pushing the 1 1/4 ounces of shot being 12,600 pounds!!! There were plenty of lighter loads being offered, but American shotgunners being what they are, I'm sure many were opting for the heaviest loads available. The same situation held with the 16- and 20-gauge shells. The "standard" 2 1/2 inch 20-gauge shells and the "standard" 2 9/16 inch 16-gauge shells carried slightly milder loads than the extra cost longer shells in 2 3/4, 2 7/8, and 3-inch lengths.
Many folks believe that the "modern" shotshells loaded with progressive burning smokeless powders, introduced in the early 1920s, Western Cartridge Company's Super-X loads leading the way, were higher pressure than the old bulk and dense smokeless powder loads. Reading period literature, this is not the case. With progressive burning smokeless powders they were able to move out equal shot loads at higher velocity or a heavier shot load at equal velocity, but at lower pressure than the old style bulk or dense smokeless powders.
I've picked up a little 96-page Du Pont Smokeless Shotgun Powders booklet written by Wallace H. Coxe, Ballistic Engineer, Brandywine Laboratory, Smokeless Powder Department, copyright 1928. It is primarily about Du Pont Oval progressive burning smokeless powder, but does a lot of comparisons with earlier style bulk and dense smokeless. As a Du Pont Oval example, he states on page 25 -
"Du Pont Oval can be loaded with 1 3/8 ounces of shot in a 12-gauge shotgun to develop the same velocity and pressure as obtained with a load of 3 1/2 drams of Du Pont Bulk Smokeless Powder or 28 grains of Ballistite and 1 1/4 ounces of shot. The relation naturally holds with other charges, but as Du Pont Oval is used principally for maximum loads the comparison is more striking as it shows the possibility of using a heavy load with Du Pont Oval that would be an abnormal load were it used with Du Pont Bulk Smokeless, Ballistite, or other existing old-style types of shotgun powders. As the pressures developed by this load of 1 3/8 ounces of shot with Du Pont Oval are the same as the pressures developed by 1 1/4 ounces of shot with 3 1/2 drams of Du Pont Bulk Smokeless, or 28 grains of Ballistite, it is impracticable to increase further the weight of shot charge with DuPont Oval. It is not advisable to load ammunition to the limit of safety of a shotgun for the reason that the pressures at this high level will ruin the pattern percentage developed by the load."
IMHO those Damascus barrel warnings that began appearing on shotshell boxes by the early 1930s were more a thinly veiled attempt to coerce shooters into buying new guns, though they probably did have some relavence to all those cheap Belgian imports that came into North America from 1880 to WW-I. All the major U.S. manufacturers guaranteed their Twist and Damascus barrel guns for nitro powders. Most U.S. manufacturers dropped their composite iron and steel barrels when the sources of the rough tubes dried up with the outbreak of WW-I, but at least Parker Bros. continued to offer them into the late 1920s. There is at least one late Parker Bros. double with Bernard barrels, vent rib, beavertail forearm and single selective trigger known.
All the above being said, I don't mean to imply that any given gun is safe to shoot. No one can tell you over the internet that a gun is safe to shoot and with what ammunition. Only a competent gunsmith (not as many out there as you might like to think) with the gun in hand, can make that assessment!!