You do not add copper to steel, for the most part. It produces undesirable properties other than corrosion resistance in certain applications (Cor-Ten). What you have said about tempering applies only to plain carbon steel, like 10100. Alloy steels, like HSLA or Tool steels, are different animals entirely.There is a remote possibility of making a spring of sorts out of brass. With working with copper or brass; to soften (annealing) it a person would heat it and quench it in water. As the metal is worked/hammered; it would harden and eventually become brittle. The opposite happens with high carbon steel. You heat it and quench it to make it very hard = brittle. To soften it you would apply “controlled heat” by either a temperature controlled oven or the old method of polishing the item and applying heat to it over a forge fire or torch. Then watching the colour change. As the metal is heated it goes through a series of colours. Purple is the desired colour to attain a spring. As soon as that happens; quickly quench it in oil to halt it at the spring stage. I’m guessing that you could obtain some springiness by “controlled” hammering.” I think the springiness would increase with usage. The formulation/% of copper to steel would have to be pretty precise to attain consistent results.
In terms of the alloy systems involved; brass is a eutectic, and steel is a eutectoid. Very, very different.