The stress to the action is based on pressure --- pure and simple....
....Pressure acts on recoil only as it causes acceleration of the ejecta and the resultant muzzle velocity....
....Since the gun has no non-trivial moving parts, recoil is identical to the ejecta mass and the muzzle velocity....
On the first point, just for conversation and relating back to the original post. Let's say a six thousand psi shell and an eight thousand psi shell fire the same payload at the same muzzle velocity, that's a 33% higher pressure developed against the gun components, admittedly over a shorter duration. I can understand that the simple answer would be that any old gun can handle 8K psi, but could that percentage of 'stress' increase on an action matter?
And on the second point, if pressure affects acceleration, wouldn't the rate of acceleration be greater for the higher pressure shell? It would, again, be for a shorter duration, and in the end the area under the high and low pressure curves, the force, would be the same to result in the same muzzle velocity.
Though 'recoil' is identical for both shells that generate identical velocities, can the human nervous system detect that brief period of a higher rate of acceleration? Are some 'mild' loads able to 'pop' a shooter's shoulder and cheek sharper than others?