American Rifleman, April 8, 1915, Fred Adolph, “More About Gun Barrel Steel”
https://books.google.com/books?id=EpcwAQAAMAAJ&pg=PA25&lpg
“Krupp makes 200 kinds of steels”

How did Krupp convince buying customers they had a steel perfect for the intended application? By chemical and physical property analysis, and no doubt performance. Crude analysis had been available since the 1860s.

The Journal of the Iron and Steel Institute, Volume 31, Issue 2, 1881
“Application of Solid Steel to the Manufacture of Small Arms, Projectiles, and Ordnance”
https://books.google.com/books?id=BCJDAQAAMAAJ&pg=PA456&lpg

The Mechanical and Other Properties of Iron and Steel in Connection with Their Chemical Composition, 1891 includes analysis of small arms gun barrel (not cannon) steels
https://books.google.com/books?id=-c8xAAAAMAAJ&pg=PA30&dq

The numbers were obviously not as accurate as those derived by Optical Emission Spectroscopy (OES), and were an average of samples.
And OES today measures other components not measured in 1880; Silicon, Chromium, Nickel, Copper, Moybdenum, Columbium, Titanium, Aluminum, Tin, Tungsten, Vanadium & Cobalt

Pre-WWI Krupp Gun Barrel Fluss Stahl was reported as:
Carbon - .45%
Manganese - .7%
Phosphorus and Sulfur both < .035%
But obviously that may not apply to 1890s Fluss Stahl or post-WWII Fluss Stahl

With the 1933 National Industrial Recovery Act the American Iron and Steel Institute began publishing “Steel Products Manuals” with the “Steel Code Tables”. The Society of Automotive Engineers also published a “SAE Handbook” with a similar numbering system, and in the early 40s the tables became the SAE-AISI Code Designations.
The standards are reported in a range; this is the industrial standard for AISI 1020
Carbon - 0.17 - 0.23%
Manganese - 0.3 - .6%
Phosphorus < .04%
Sulfur < .05%

So if a paying customer specified .2% carbon gun steel, within the specified range is what they got. And the physical properties thereof would help confirm the quality thereof.

To argue that even at the turn-of-the-century the purchasers of steel products had no idea what they were buying (and didn't employ chemists and metallurgists to confirm) is just silly.