Metallurgy gives the maximum weight budget for given delta pressure and given buoyancy for all non pressure vessel equipment.Unsurprisingly, Metallurgy again dictates Hull strength and therefore Max dive depth of the Submarines.
Japan, Germany and US continue to remain at the forefront of this (obviously). Russia sidestepped (kind of) by application of its vaunted Titanium reserves.
But is Mariana trench the limit for deep diving?
Other than the Hull strength (dictated by metallurgical progress), there is another factor that might (? When factoring in the costs sunk on the Metallurgy and manufacture of a submarine) prevent nations from demanding that Submarines dive deeper. The SOFAR channel.
The SOFAR channel is a particular depth at which sound is able to propagate at great lengths (because of the conflux of certain factors like pressure, temperature and salinity which in turn affects sound wave propagation). Usually it's about 600 to 1000 m depths.
The relationship between the diving deep at constant pressure vessel mass given by the specific strength of the given wall material.
Now, the rules can be cheated by :
1. automate as many system as possible, and pressurise the non human occupied segments with helium , with half strength vessel wall compared to the target diving deep. Means if the 25% of ship is atmospheric, then the pressure full vessel wight can be decreased by 40% . Problem it require lot of automation, like on the Russian submarines.
2. Pressurise the whole ship. With nuclear propulsion it is not a big deal, and can give few hundred extra meters of diving deep. Problem is the crew can't escape the ship by surfacing and moving to inflatable boards - it require pressurised escape crew capsule, like on the Russian /Soviet attack submarines .
3. Use high tensile strength pressurised carbon fibre tanks to get extra buoyancy , but it means of course if the extra tank damaged then the ship sink like a stone.
Above can increase dramatically the diving deep, but of course it complicate the design and makes it very expensive.