Realize that when the procjetile clears the muzzle, the entire barrel is full of gases. They continue to exit & pick up speed in doing so. The gun may well continue to accelerate for a teeny weeny micro second longer than the projectile, but it will be so continuous, & in the same direction, you won't actually feel it as a separate component as with the rocket launcher example. It will just be a part of the recoil.
It is though noted that powder charges in proportion to total load are normally quite small in a shotgun. Compare for instance a 1oz load in a 12 gauge total wt of shot, wads & powder may reach 500 grains. If the powder charge were 20 grains then it would make up only 4% of the entire weight to be ejected. On the other hand if we took even the low powered .30-30 with a 150 Gr bullet & a 30 Gr powder charge the powder makes up 16.666% of total ejector wt. Thus the ejecting powder gasses from a .30-30 make up a higher portion of the recoil than do the gases from a shotgun. You still however do not "Feel" them separately, but just as a single "Kick". If we went to a larger .30 cal cartridge which used a 180 gr bullet over 60 grs powder then the powder is a full Ľ of the total wt. This is why recoil reducers
(muzzle brakes) are so much more effective on rifles than shotguns. Even so their is a small component of gases exiting the muzzle after the wad has cleared & this does contribute to the recoil.
