No expert, but I think butt welding it would just anneal (soften) the spring steel rod at the joint. It may eventually just bend (twist) at the join. Or it might be fine.
A better way might be to make some kind of tube sleeve with 4 welded on nuts. The rod ends could slide into it and be pinched by bolts tightened through those nuts.
Regardless, if welding you might want to use a short section of L channel across the rod to back and support the weld joint.
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