I know the joke is that guns are pointless in the hadal zone because cthulu lives there, but...

A gun being wet or immersed in water rarely makes it totally incapable of firing at least once.

Many modern firearms will fire a projectile at lethal (to a human) velocities while underwater, though range and accuracy will be greatly reduced.

Getting a gun wet generally does not make it ineoperable.

The primer and gunpowder combust and deflagrate without the need for external atmospheric oxygen, they contain their own oxidizers.

(This also enables firearms to function in space, with no atmosphere)

The main problem is that if the gun's barrel is full of water, this provides significantly more resistance than a barrel full of only air.

The cartridge will fire, but the bullet's velocity through water will be much lower, the weapon might not cycle its action properly (meaning you may have to manually do so)...

... and the overpressure will cause significant damage to the weapon, possibly leading to it explosively dissambling itself after sustained overpressure usage.

Which is actually comparable to running a bunch of overpressure, magnum or +P rounds through a firearm above water.

There exist firearms and specialized cartidges (flechettes or otherwise) that are designed differently to operate consistently while underwater, as well as 'amphibious' firearms that work decently well submerged and not submerged, used on ambibious vehicles or by waterborne commandos like the Navy SEALs.

https://en.m.wikipedia.org/wiki/Underwater_firearm

Probably what is more common is a speargun, which usually is not a firearm, just releases a bunch of compressed gas of some kind to fire a spear... somewhat like a paintball gun/marker.