"Eventually" stumbling onto a nuclear sub will be difficult past the 1st Island Chain.
Also, my understanding is that surface ships operate by sprinting and then drifting silently to allow their towed arrays to work.
If you have SURTASS ships, SOSUS and enough sea gliders around, they can cue up MPAs to more specific areas to search. The 093s can cue up searches also. Otherwise, your ASW operation is pretty much limited to area where you can maintain air superiority. And you need a lot of them to stumble onto quiet submarines.
So for PLAN, I'd imagine they can find subs all the way down to Spratleys. Beyond that, they will have to rely on helicopters and all the sea gliders they've been out there. Indonesian fisherman found sea gliders all the around java island. So, PLAN is really trying to map out that entire area. Keep in mind, US/Japan did the same thing to China with their own East Asia SOSUS.
If I were China, I'd be developing technology that destroys US/Japanese SOSUS.
For China, they are going to also be relying on SURTASS, SOSUS, UUV, these floating sensors
China is building SOSUS all the way out of Guam, Palau and south Philippines. You can see that as they are building a blue water navy, they are able to build these passive sensors further out, past the first island chain. So with enough effort, they may have enough sensors from Kyushu down to Philippines Sea to give the surface fleet more space to work.
Without cuing, it's really hard even for MPAs to find submarines. Stumbling into is probably the right phrase!
It seems to me as time goes on, low cost AUVs and UUVs are going to be a huge part of your ASW and MCM effort. And they can cut underwater cables and destroy other countries' SOSUS web.
Keep in mind that even a loud 093 has certain advantages over the quietest Japanese diesel subs. They will carry more power sonars and have a larger crew. They can stay protected with their CSG. And they can move so much faster than the diesel subs that as long as China has air/surface superiority, 093s would have the freedom to finding diesel subs and hunting them down.