Bro. Nudge: I know next to nothing about rifle barrels.
A barrel is typically a deep hole with steel wrapped around it. A rifle barrel has some spiral grooves to impart spin to the projectile to stabilize it.
Your copy-and-paste research confirms that barrel makers used a lot of different steels to make perfectly usable shotgun barrels. They range from low carbon 1015 to much higher carbon 1045. And there was wide variation in composition, even in barrels used by the same manufacturers, over time. That kind of confirms my statements saying that your very small sampling and metallurgical testing tells us very little at all.
But I suppose it looks impressive to those who know nothing about steel, and next to nothing about rifle barrels.