There IS a procedure for welding “spring steel”.
Usually the parts being welded are pre-heated in the area of the weld (for depth of weld penetration) but this isn’t always necessary. The act of welding will anneal the metal at, and immediately around the weld joint, causing the metal to soften (that’s where and why the joint will fail, just off to the side of the weld intersect). Often, a welded piece will suffer another break later on, not precisely at the original weld joint but off to the side (where it was softened). The weld itself is usually harder than the original metal.
The way the newly welded joint is made hard again is to broadly heat the newly welded area to a specific temperature or color (most heat treaters go by the color of the metal) and then quickly quench it in oil to rapidly bring the metal temperature down and that process re-hardens the metal. But this is a relatively precise process to get the hardness that you want in the finished spring steel piece (sometimes a durometer is used). Too hot makes the metal very hard but brittle and will more easily break. Not hot enough makes it softer and it will bend/break. The usual process is weld the ends onto your bar, then heat the entire bar to a specific color, then quench the whole bar in an oil bath. That will make the whole thing the same.
IIRC, there are special welding rods for welding spring steel. Your local welding supply shop should be able to help with what you need.