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since part of the energy is being used to work the action the recoil should be less.
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True, part of the energy is being used to work the action, BUT, ALL the energy is still there. Part of it is doing something in an auto pistol, on its way back to your hand & wrist, but its still all there.
Because it is spread out (time wise) you feel it less, but its still all there.
Newton's 3rd law (equal and opposite force) means launching x weight at abc speed generates a given amount of recoil. Pistol or revolver, the force is the same when fired. The differences in weight, height of bore axis over grip, shape of the grip, and the rate of recoil impulse transfer make a difference in what you feel when you shoot. The energy a semi uses to unlock, push bak the slide, compress the spring, etc, still all transfers to your hand, it doesn't just vanish into thin air, it just gets to your hand after it does the work, compared to the revolver (or single shot) where all the energy arrives at the same time.
Now, we aren't talking about much of a difference in time, not enough to notice with merely human senses (or at least my human senses), and we generally perceive the more "spread out" recoil as less recoil.