If it's a staff cap it's an officer's and privately purchased, not issued by the army. In any case, since foraging was not one of the duties normally expected of a staff officer, it's not likely the button attachments were especially strong so he could do a better job of it than enlisted men...
Officers were expected to purchase their uniforms, so of course they weren't issued. The hats nonetheless had to meet army specification, so differences in construction were no more significant than variations of the issue hat, which itself varied quite a bit.
Nobody here has suggested that a forage cap was used for command-assigned foraging duty. They weren't designed for that. Too small-scale for that. But did a few officers of either side use their caps to grab some elderberries on the way back from the latrine once in a while? Sure. Nothing to blow whistles over.
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