Some updates on the SSK-N:
Both
and
on Weibo have claimed that the SSK-Ns (nominally named the Type 041-class) are already under construction.
It is mentioned that there would be 4 boats for the 1st batch of the 041 SSK-N, with the order equally split between Jiangnan and Wuchang.
Both of them also claimed that there are photos (satellite-view and/or ground-view) which proves the above to be the case. However, until now, I'm still unable to find it, so if anyone manages to get their hands on those photos, kindly share it here.
The Army Recognition website has also reported on the matter: