From GameWatcher: “The Sinking City may not focus much on combat, but the Shotgun is an extremely useful tool to have regardless. In this article, we’ll teach you how to get the Shotgun in The Sinking City, so keep reading!
It just so happens that The Sinking City Shotgun is the ultimate close-quarters firearm, and since you’ll mostly be facing off against Lovecraftian creatures in close-quarters combat, it’s invaluable for your progress.”
Source: N4G PC The Sinking City Shotgun Location Guide