Yes. I do think China pays around $400M per boat, whereas the $625M price for Pakistan includes support and local production.
If we compare the the Type-52/Type-55 versus the equivalent AEGIS destroyers from US/JP/KR - we can see Chinese ships have a significant cost advantage.
That should carry over into the realm of submarine construction. So Chinese SSKs should be much cheaper than Japanese SSKs.
Again PLA needs to provide support for their own submarines too, and probably to a higher standard.
There are "tricks" state owned companies can use to drive down the per piece cost for their own hardware (such as filing much of the costs under another category, or taking pay directly from the state budget instead of marking it as part of a purchase). China can technically pay 0$ for everything since all of the military contractors are state owned, they would just have to shift all the bills as national spending. This doesn't fundamentally change the real cost of the item in question.
Even if we arbitrarily shave off 225 million off the 041's price, it still won't be "much" cheaper than the Soryu, only marginally so. And it would still be more expansive than a Type 212.
If that carries over to SSN pricing, it would mean either slightly more expensive or about the same. TBH I need to correct my last post because it's not going to cost 6 billion like the Seawolf, since that was apparently due to some mismanagement leading to runaway costs, but 3 billion + like the Virginia could be expected.
An Astute is cheaper because it has no VLS. It's possible China could go all in on stealth and forgo the VLS, which could further bring down price to 1.5-2 billion.