688i level isn’t that quiet though. Even the improved Akula is generally considered a little quieter than Shang.
The main divergence from the US and Russia seems to be that after designing their “Los Angeles level” submarine, China went ahead with a next generation diesel submarine instead of making a Seawolf/Yasen equivalent.
I see it as a (short term at least) rejection of the nuclear submarine concept.
Quietness seems to be the no 1 factor for the PLAN which doesn’t need to constantly patrol faraway seas or strike land targets with subs.
Edit: It could be that PLAN SSNs are mainly aimed to be rapid response forces against the Indian navy, which doesn’t require very powerful boats.
China's progress with SSK development and new variants does not mean they are not pursuing next generation SSN capabilities.
We all know that next generation nuclear submarines are in the works for both SSN and SSBN roles.
But we have yet to see it emerge yet.
The fact that 09III variants are being produced in limited numbers means they have yet to reach a level of capability that will satisfy the PLAN for mass production. It took many iterations until the PLAN reached 052C and then 052D that satisfied their requirements and they were happy to procure large numbers.
It would be like suggesting that the limited production runs of destroyers prior to 2010 when 052C production restarted and 052D production subsequently began meant that the PLAN was "rejecting" the destroyer concept. No, it just meant they were waiting for a ship type that could meet their requirements before building them in large numbers.
Looking at PLAN requirements one can easily see that they have a requirement for a fleet of a couple dozen high performance SSNs at the least, to complement a large number of capable SSKs as well.