Production can only increase after the first 095/096 or any other next gen SSN/SSBN is built and finishes trials. This is how they did it with the 093. The jump to 095 is likely to be as big a technological leap as the 093 was over the 091. That's why I think the initial production rate will be quite low, despite the size of the facility.
As Tam has written, using the original 09III as an example may not be accurate.
For one, the 09III itself seems to have undergone multiple revisions or variants. Including the original baseline variant, there are five unique configurations of it that have been IDed (see picture below). Now, we don't know if all of those are unique hulls, but I wouldn't be surprised if most of them were. Considering past PLAN practice with the 052 and 051 classes and successive variants, chances are they were introducing successive new technologies to each of those 09III variants. There is also the yet to be seen 09IIIB variant that has consistently been described to have a VLS.
What that means for 09V, is that the "leap" to 09V isn't from the original 09III, but rather through various different variants of 09III, including the much spoken of 09IIIB.
There is also definitely precedent for going to mass produce 09V without first producing a limited number to test them; as Tam mentioned for surface combatants and destroyers in particular. For example the 055 as a brand new clean sheet class was mass produced from the outset. The first has yet to be commissioned and already six hulls have been positively IDed with more confirmed to be on the way.
Whether the Navy ends up ordering a large batch of 09Vs from the outset will depend on the capability of the submarine, and overall confidence and maturity of the technology behind it. Do I think the industry is ready for that? Hard to say. However if I were the BHSIC, the Navy or the Chinese govt, I wouldn't have signed off for such a large expansion of nuclear sub production capacity if I didn't think that they could start making use of it fairly early.
If my goal was for them to produce a small number of a new class first and then eventually mass produce it after they are confident in it, then I would've also delayed the new production facility construction as well
They will also need to train enough crews first.
Regarding crew; of course they will. However that's far from a unique challenge for the PLAN. A decade ago they only had two true aegis type AAW destroyers in the form of the two 052Cs, yet they've clearly managed to scale up and proliferate that expertise to be able to greatly expand the number of such vessels in service today and into the future.
Regardless of the initial production rate, however, peak production rate will depend on how many SSNs bohai has been contracted to produce by say the mid 2030s, and that definitely would be a factor that determined the size of this facility. But has Bohai provisioned the facility for being capable of handling a possibly higher production rate, that is the question for me and I think it has.
If such a large facility had been built for them then undoubtedly provisions would've been made for the full extent of the facility to be capable of being used if needed.
The question, as I wrote before and as you've written here, is when or if the full potential of the facility will be utilized.
Is there any facility that assembles subs the way JCNX assembles its destroyers? If there is, then that would make things very interesting, otherwise i'm still leaning towards the subs staying in one slot for the duration of their assembly.
There aren't many submarine assembly halls like what we see at BHSIC. If you look at Newport News, General Dynamics Electric Boat, they are only "long" enough to accommodate a single SSN or SSN/SSBN respectively, they simply lack the length to accommodate two SSNs in series like BHSIC can. They are assembled in a way that they are "fixed" in a single slot from module arrival to module assembly to launch.
However, the UK's BAE facility at Barrow in Furness is quite close to what I described for BHSIC. If you look up images of Astute subs being constructed there, you can see how they have modules transported to each "line" within the building and they are gradually assembled together and the submarine moves forward along the line before it is eventually launched (pictures below).
(edit: Sevmash also has an assembly hall large enough for comparing with BHSIC but there are few if any pictures of submarine assembly in Sevmash that I could find).
Of course, the Astute class production is not quite the same as what I envision for BHSIC, because BAE are building only a limited number of Astutes because of a limited RN order for them. Chances are they aren't using the full capacity of their facility, and there's a lot of free space to go around; whereas for facilities like Newport News they clearly are able to assemble an entire SSN in a single "slot" that is only one SSN long, whereas BAE's facility is similar to BHSIC's in length and able to theoretically accommodate two SSNs in series.
By the way, what I described regarding ships or submarines being assembled to a stage and then moved is not rare. It's fairly common for semi complete ships to get moved along a rail from one part of a shipyard to another part of a shipyard for a next stage of work. Not every ship is built inside a drydock in a fixed position. Even some ships like DL's destroyers are moved from one part within the drydock to another part (recall the current two 052DLs in the mega drydock at DL were moved to their current position only after the first two 055s were launched).
The fact that we rarely see submarines built in such a fashion is probably because there are few shipyards in the world with such extensive and large facilities to allow it. However, all submarines that are assembled on land and not in a drydock have to be transported on a rail from their assembly position to a drydock for launch anyway. So what I'm describing regarding a submarine being moved between positions as it moves from one stage of assembly to another is really just using the standard practice for submarine transport for a shipyard but applying it before the entire submarine is ready to be launched. It's also no different to transporting modules from a fabrication area to the assembly area like standard submarine yards.