Have been working on barrel steel composition for a long time, and thought I'd post the information I have so far. Other opinions are of course valued.

Winchester Standard Ordnance Steel used on the Repeating Shotgun Model of 1893 and (initially) the Model of 1897 was very likely “cold rolled” Bessemer/Decarbonized steel with an ultimate tensile strength of about 60,000 and yield strength of about 40,000.

1902 "rolled steel barrel"

1909 Sporting Life Winchester 1897 ad with "Winchester Rolled Steel"

Winchester Nickel Steel was introduced for the Model 1894 rifle about 1896; with a reported ultimate tensile strength of 100,000 - 107,000 psi with an elastic limit of 81,000 psi.
Ordnance steel was initially used on the Model 12, then Nickel Steel until 1926 when it was discontinued, reportedly for corrosion and barrel failures, and was replaced by an unknown composition “Winchester Stainless Steel” with a “Japanned” (black lacquer) finish. - ?Krupp Chrome Nickel?

Winchester “Gun Barrel Nickel Steel” for rifles was surely different that the nickel steel used in shotguns
“Report of Heat Treatment of Barrel Steel Rolling”, 1902
From Bethlehem Steel Co.
Carbon - .50%
Manganese - .77%
Phosphorus - .026%
Sulphur - .037%
Nickel - 4.0%
Chromium <.01%
Molybdenum <.01%
Tensile Strength - 107,000 psi

Midvale Steel Company c.1900 Nickel Steel
Carbon - .59%
Manganese - .765%
Phosphorus - .027%
Sulphur - .03%
Nickel - 1.57%
Chromium - .065%

I have found no composition report for shotgun barrel Winchester Nickel Steel, but it was likely AISI 2330 with a nickel content of 3.25-3.75%, carbon content of about .30%, and ultimate tensile strength of about 110,000 psi.
AISI 2317 has a carbon content of about .20% with a tensile strength of only about 60,000 psi.

Winchester Proof Steel (AISI 4140 or possibly AISI 4340) was introduced in 1931 for the Model 21 and in 1932 for the Model 12; with a reported ultimate tensile strength of 115,000 - 120,000 psi and an elastic limit of 105,000 psi.

Edwin Pugsley in a letter to F.W. Olin April 11, 1932 stated:
Both (Model 21) frames were heat treated, then one was case hardened and the other blued. The case hardened frame had a tensile strength of 94,200 psi, an elastic limit of 85,400 psi, and elongation of 2%. The blued frame had a tensile strength of 174,600 psi, an elastic limit of 160,950 psi, (and) an elongation of 12%.

An undated document, presumed to be from the 1930s in The Winchester Model 52: Perfection in Design by Herb Houze on p. 92 states that barrels used in Winchester rifles and shotguns have a tensile strength of 129,150 psi and elastic limit of 112,500 psi, but there was no mention of the steel composition.

Winchester catalogs in the 70s state Proof Steel was “cold forged Chrome Molybdenum”.

Winchester's Finest The Model 21 by Ned Schwing states Chrome Molybdenum alloy.

Other sources state “nickel-chrome-moly alloy steel”.

Summary of “cold rolled” barrel steel tensile strengths.
All can be heat treated for different applications (rifle receivers) to much higher strength, and yield strength matters also.
AISI 1005: 40,000 psi
Twist and Crolle Damascus: about 55,000 psi
Winchester Standard Ordnance and other "cold rolled" Bessemer/Decarbonized steels and AISI 1020: 60,000 psi
c. 1900 “Fluid Steel” (Siemens-Martin & Krupp Open Hearth Steel AISI 1021-1034): 75,000 – 85,000 psi
AISI 1140: 85,000
Krupp Fluss Stahl (Homogeneous Fluid Steel) was introduced about 1890 and by reported composition was similar to AISI 1045: 85,000 psi.
AISI 1040 (and modified), Bohler “Blitz”, 4140 Chrome Moly (not used until after 1930s): 95,000 – 100,000 psi
Winchester Nickel Steel and Marlin “Special Smokeless Steel”: 100,000 – 105,000 psi

When discussing the use of Nickel or Proof Steel with steel loads, it is helpful to compare the hardness of the historic and modern shotgun barrel steels:

Rockwell B Hardness…..Brinell Hardness
(All numbers for non-heat treated cold rolled steel)
Grey Cast Iron – 63……………100
Wrought Iron – 65……………..105
AISI 1012…………….…..……...105 (likely similar to damascus barrels)
AISI 1020 – 68……..…………...121 (the usual pre-WWI barrel)
AISI 1030 – 80………..………...149 (commonly found post-WWI +/- low alloy)
AISI 8620 Ni/Cr/Mo – 80…..149 (used for modern doubles' frames)
AISI 2330 Ni – 86…..….……….167 (Ni = 3.25-3.75%; C = .28-.33%)
AISI 2340 Ni – 92…..….……….194 (C= .38-.43%)
AISI 1040 – 93………...……….. 197
AISI 4140 Cr/Mo – 93…….....197
AISI 4340 Cr/Mo/Ni – 96…...217

Steel shot is about 95 Vickers DPH = 52 Rockwell B = 85.5 Brinell. Hevi-shot is harder. 5% antimony lead is only 9.5 Brinell; 3% 7.76. NICE shot about 15 Brinell.

Current manufacturers do not reveal the composition of their steel load compatible barrels. The Beretta website states that “Steelium/Excelsior HSA Steel (is) proprietary tri-ally steel (Ni/CR/MO)”

Carlson's is willing to disclose the composition of their Benelli Nova and Remington 870 replacement barrels and they are AISI 4140. Their barrels in the past were made by Verney-Carron SA, but the website does not now state the maker.

When the Benelli M1 Super 90 was introduced the barrels were advertised as 4140.

SO barrel steel composition is only one factor is steel shot compatibility; the others being the design and engineering (wall thickness, profile, and esp. choke constriction), fabrication, and proof testing thereof; and the modern thick plastic wads.
Despite the anecdotal testimonies, I have found no statement that Winchester Nickel Steel may safely be used with steel loads.

With the appropriate choke constriction, it would seem reasonable that 4340 Winchester Proof Steel CAN be used with steel loads.

Possibly we could skip the "steel sucks" verbiage - that's not the topic of the thread.