Normal US Navy subs only dive to 500 meters. The Titan dived to 4000 meters. Not sure if you would use the same steel as for a regular sub. France and Russia have submursibles that could dive to the Titanic. If the US has them, it is very secret.
I think you are a bit confused. No country has a military sub that can dive to that depth. Any vessel that can is in the research class with some entering into a commercial classification, while yes they are sponsored by a country sometimes, no they are not military.
Yes, the US sponsors research like France and Russia with ultra-deep dive submersibles.
The Triton Submarine, an American-based company in Florida created the first manned submersible to reach the deepest part of the ocean in the Marina Trench, that was back in 2019.