You can get a chemical assay to at least tell you what the exact material is, but there isn't much to tell you how it was heat treated

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All steels will deflect the same amount, it has to do their modulus (being Fe based) and not the composition or strength.
You can test its hardness to get an idea of the strength level. Depending on the strength there may be more than one option for heat treatment.
You will need a real chemical test (including C) in order to know the alloy though.

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P.E. Metallurgy

As EdStanilees said, you cannot identify the steel using the deflection.
Hardness plus a metallography could give you an idea of steel grade and heat treatment.

The E of steel alloys does vary. I recall seeing from around 27E6 psi to nearly 31E6 psi. However chemical analysis will be the only method to be sure of the composition. As far as I know hardness / heat treat doesn't change E a noticeable amount. In practical use very small changes in section or geometry are so much larger that most everywhere I've seen deflection calcs being done they just went with 30E6 psi, no matter the steel alloy. It also varies with temperature.

https://amesweb.info/Materials/Youngs-Modulus-of-S... which references:

Metals Handbook. Properties and Selection: Irons, Steels, and High- Performance Alloys. ASM International, 1990.

The low C steels (0.20% C max) are slightly lower E than higher C grades.
For spring work we always used 29.5e6psi, since that is the value for any high C steel at 200F.
Heat treat doesn't matter, but severe cold work (>40%) can raise it some.
For SS and low C steels we used 28e6psi.
If someone really cares I have the ASM handbook of elevated temperature properties and I can look them up by alloy and temp.

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P.E. Metallurgy

1) Variations in E between carbon and low alloy steels are almost trivial. The information can be found online.
2) The bottom line for spring design (barring corrosion resistance considerations) is the shape and the strength, as indicated by hardness. Processing is key to achieving uniform properties, freedom from surface discontinuities, and absence of decarburization.
3) Strength can be achieved with a variety of alloy compositions, but there are a limited number of steel grades that find application for springs. ASM Handbook provides good information.
4) Your application should dictate the design and alloy selection. I would begin by finding out what folks are using for similar equipment; i.e., what the industry standard is.

All you really need to do to characterize your sample is chemical analysis (not PMI) and hardness testing. Pay attention to final coating for corrosion resistance. The life cycle of a spring very often includes a corrosion pit, which acts as the initiation point for fatigue fracture (with fatigue fracture, discontinuities trump all other considerations).

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

Looks like Phil has a vested interest in XRF, based on his tag. No, XRF would not be suitable because full quantitative is necessary, especially for carbon, as that part of the component. There are specs ASTM specs for spring steel, especially if we are talking wire used for coil springs. These typically call out tensile properties based on wire size, but I have had very good correlation in those instances in using Vickers hardness and converting to tensile strength via ASTM A370 for ferritic steel.

All true mrfailure.
PMI is NOT equivalent to chemical analysis, which is what is required here. You can search eng-tips for my previous rants on this subject.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."