> The published data for military submarines is the nominal test depth, not the actual design limit. The operational depth may be much deeper but that will be classified.

We know the actual collapse depth for an older sub: 730m for the USS Thresher (test depth: 400m), in 1963.

Test depths of current generation subs are ~20% higher; pushing them to 700m or so might be plausible, but not much more. Radical hidden capabilities would either require substantial advances in material science or drastically different hull thickness, neither of which is really feasible to hide from adversaries anyway, especially considering how little utility you get from hiding this (compared to e.g. exact capabilities of anti-air interceptors or radar characteristics for bombers/fighters).