But isn't some of the bullet's energy lost into the recoil that cycles the slide?
No. My understanding is that the recoil is the "equal and opposite" force - the reciprocal, as it were, to the energy that propels the bullet. There is no way to reduce that energy (for a given mass and charge), or to add it to the energy that propels the projectile. “For every action there is an equal and opposite reaction.” The recoil energy is either transmitted to the shooter’s hand in full (as with a revolver), or a portion of it can be harnessed to cycle the slide on a semi-auto. Absorption of a portion of the recoil energy by the moving slide lessens the remaining recoil energy felt by the shooter, even though there is no loss of gas in the barrel of the semi-auto.
Felt recoil does not determine the velocity of the bullet. Given two guns of equal barrel length but of different weight, both firing the same weight bullet under the same charge, the muzzle velocity of each bullet will be the same from each gun, but the felt recoil will be greater in the lighter gun. However, the Total Recoil Energy is the same for each gun.
A gas operated recoil system actually bleeds off a small portion of the gas as the gas is propelled through the barrel. The energy of the escaping gas is absorbed by the bolt, or slide, as it travels rearwards. Both contribute to lessening felt recoil, but in this case, unlike a pure recoil operated semi-auto, energy is diverted from the job of pushing the bullet down the barrel. So in a gas operated recoil system, there is less energy to propel the bullet - but not because of a reduction in felt recoil, but to an actual loss of propellent (gas) energy.