A 20g Field SN 14788 shipped October 21, 1919 is the latest Damascus barreled gun known, but Damascus barrels were still listed as an option in sporting dealer catalogs into the late 1920s.
1918 E.C. Simmons, St. Louis
"Fine Damascus" still available for 16g hammer guns
"Nitro Steel or Damascus" still listed in the 1928 Janney, Semple, Hill & Co., Minneapolis, MN catalog
It is very likely that all the "rough forged tubes" were used up by that point however; very few were produced in Liege after WWI and the last by J. Delcour-Dupont, Nessonvaux in 1930.