Shotguns are very low pressure as compared to pistol or rifles. Which is why shells can be made of paper and plastic, with only a brass rim to aid extraction. (the new super-poylmer .223/5.56 NATO notwithstanding…) The steel in shotgun barrels is way thinner, and the wide bore holds and has to move lots more water when it was fired.
It all adds up to "KB!".
I would be surprised if most recoil operated autopistols cycled reliably under water. When the slide and barrel recoil, the slide has to squeeze the air that's around and under the barrel in the dustcover area out through the gaps with the frame and the ejection port etc. The much higher viscosity of water means you get a much lower slide velocity. The pistol they used looked like a SIG-Sauer, and the slide rides inside and outside of the frame, which means the water has less room to escape.
A Glock has a pretty big frame to slide gap, so perhaps the water can squish out of the way easier. However, I've never heard if the Glock would cycle reliably underwater or not. Just that the famed Glock "Underwater striker spring cups" were little gaskets that kept the water out of the firing pin channel so the striker velocity would be high and not have water in the channel slowing it down. Even then, it was a reliability enhancment, not a guarantee. The SEAL or SCUBA commando or whatnot was still supposed to rise out of the water before firing. It was just so they could fire instantly, without waiting for the Glock to drain.
AFAIK, the spring cups weren't meant for underwater "James Bond" SCUBA battles etc.
The Russian APS that fires long, thin, "bullet-darts/flechettes" is another story though. HK made a little proprietary pepperbox multi barreld pistol that shot similar ammunition too.
Every time they said "Salami Rocket" or "Meat Rocket"I just laughed like Beavis & Butthead. I couldn't help it.