I have a feeling that some people here may have been idealizing the SSK-N a little too much.
Firstly, given that the SSK-N is to be based on the hull of the preceding SSKs (likely to be 039C), per the 2017 presentation slides:
This means that the SSK-N isn't going to be large. Taking the swapping/addition of a mini nuclear reactor or a nuclear battery into account, my estimation is no heavier than 5000 tons of submerged displacement at full load.
Besides, there are the following information from the grapevines back in 2020, which discounted the possibility of the SSK-N having VLS cells onboard:
Hence, it seems that the likelihood of VLS cells being present onboard the SSN-K (or at least in its current iteration) is rather low, based on what we've accessed so far.
Personally, while I'm not entirely against the idea of equipping SSK-Ns with VLS cells for AShMs - I prefer to see the presence of AShM-loaded VLS cells as something that is "good to have, but not needed unless absolutely necessary".
It should also be noted that the output power of the mini nuclear reactor or nuclear battery stated in the grapevine source is listed as 10MW. This is actually a far cry to the power output typically seen on nuclear reactors for proper, larger SSNs (150MW to 250 MW). That is, the mini nuclear reactor or nuclear battery only has 4% to 6.67% the output power of the SSN's nuclear reactor, despite the SSK-N expected to be only ~2-3+ times lighter than the SSNs. This should be an obvious enough difference for making further inferences and guess-works regarding the SSK-Ns.
Therefore, for the SSK-N - Regardless of whether it has a mini nuclear reactor or a nuclear battery, I would recommend seeing it as something of a "SSK Pro-Max-Plus". Namely, the SSK-N is expected to have:
1. The ability to stay completely submerged for many days or even weeks at a time;
2. The ability to travel and maneuver at relatively high speeds for extended distances while completely submerged;
3. The ability to sail very close to the seabed, hence able to hug the topographical features of the seabed which would otherwise be very difficult for proper, larger SSNs; and
4. The ability to stay really quiet when travelling at low-to-medium speeds at shallower waters, hence greater degree of stealth.
This means that instead of acting like an ac-hoc SSN, the SSK-N would be better deployed as follows:
1. Picketing/intelligence-gathering;
2. Patrolling (or outright camping) around naval chokepoints and outside of enemy naval bases to attack passing enemy warships;
3. Laying sea(bed) mines (and potentially assist in clearing enemy minefields); and
4. Conduct seabed warfare (tapping on or cutting enemy seabed communication cables, setting up own or destroying enemy SOSUS etc) -
Which can be greatly augmented by USVs and/or UUVs.
Speaking of missiles - Compared to the larger YJ-21 AShBMs, a land-attack/anti-ship cruise missile that is either dual subsonic-supersonic (i.e. YJ-18B) or full-supersonic (possibly the yet-to-be-revealed YJ-15) with 500-800 kilometers of range would be a much more appropriate choice. This is besides the fact that the former option is readily available by using torpedo tubes only.
However, given the expected characteristics and operational doctrines for the SSK-Ns - Having a module for small-size USVs and/or UUVs inserted behind the sail structure would be a better/superior warfighting capability that the SSK-N can bring to the table compared to having more AShM-loaded VLS cells. Of course, you could have the VLS cells configured to stow, deploy and recover USVs and UUVs besides AShMs, which is similar to how torpedo tubes work - But the fundamental point remains the same.