I'll see if I can get this question out, in a nutshell does the pressure affect the cycling of a gas or inertia shotgun ?
What brings this question I have one gas operated 20 gauge that is a bit ammo finicky on new factory ammo. Ammo of the same weight charge and velocity rating some cycles better than others. Is that because of possible pressure?
When hand loading you can pick a powder that has some incredibly high velocity in lower pressure or you can give some faster burning powder that gives you a lower velocity on higher pressures. That's where my question of does the pressure really affect the cycling of an auto loader.

I know it can with gas autoloaders. My Benelli inertia 28 gauge cycled my Lil Gun reloads wonderfully. When I tried them in a gas 28 I got it ran the bolt so hard/quick it wouldn’t pick up the next round. Changed my load, same weight of shot, from Lil Gun to Blue Dot and gas gun cycles wonderfully. Faster powder with less powder charge mattered!! BTW, the velocity of those 2 loads was only sboutv15-20 FPS difference.

Loading only Blue Dot now in my 1 oz 28 gauge loads as it works both shotguns nicely!
Hope this example of what can occur is helpful. I know I learned something by the time I figured it out 🤣

In a gas gun the operating factor is volume of gas. Pressure or velocity affect nothing, other than the fact that low enough pressure will cause failure.
Almost everyone thinks recoil is ls pressure related, but actually its a function of mass and velocity.

Pressure will have no effect on inertia operated shotguns, the operating factor there is recoil. Recoil starts the bolt in motion, and inertia carries it through the cycle.

HM