As you say, if the project is real then all we can assume is that PLAN has identified some cost/capability/survivability "sweet spot" where such a platform makes sense for their requirements.
The major reason for pursuing a semi-submersible design would appear to be to reduce the vessel's radar and visual signatures. It seems reasonable to assume, therefore, that acoustic signature reduction would also be a high priority, and that the vessel would therefore adopt some of the same measures that submarines do, potentially driving the cost of the platform closer to that of a submarine.
I actually don't think it would be reasonable to assume that they would seek to pursue acoustic signature management similar to that of a submarine.
Let's consider why they may be interested in reducing an arsenal ship's surface signature -- it is essentially to make it a smaller target, in domains of RCS and visual/EO, but RCS especially imo.
An arsenal ship is usually conceived as a fairly large platform given the priority of putting many missile tubes into a single platform with not much space for little else, the bigger it gets.
The bigger the target it is, the bigger the RCS and visual profile it is and the more easy it is for the current primary long range ISR/tracking-midcourse-terminal kill chain to work (with the modern kill chain largely centred around around radar platforms and fire control radars for the detection/tracking/midcourse phase, and using active radar seekers and as passive EO/IR seekers for the terminal phase). But by putting most of the ship under water, I think the goal is to significantly reduce the ship's RCS and visual profile and thus also significantly reduce their vulnerability to the tracking-midcourse-terminal kill chain at all levels in the radar and visual/EO domains. A small radar and EO/visual signature means it's much harder for the enemy to know if your arsenal ship is actuall there at long range and at the tracking/midcourse guidance phase, and it's also hard for the enemy's missiles or FCRs to positively identify and engage at the terminal phase.
OTOH, when we consider acoustic stealth requirements for submarines, it is because they rely on the ability to achieve something as close to absolute stealth as possible, which I think is quite different to the signature management goal of a semi submersible arsenal ship.
This isn't to say that they won't seek to appropriately manage the acoustic signature of such a ship -- they're definitely not going to go out of their way to make it loud -- but I think it would be acceptable for such a ship to have an acoustic signature similar to an equivalent surface ship of its size, considering it is not meant to be a submarine and that in a high intensity contingency it would likely operate in as part of a task force made up of other fairly conventional surface ships (DDG, FFG, CV) which will generate a fair amount of noise as well. As part of a task force, the idea of signature management for the arsenal ship would be to make it very difficult for the enemy to confirm whether such a ship is even present in the task force for the longer range tracking/midcourse guidance part of the kill chain, and in the terminal phase of the kill chain the goal is to make it very difficult for the enemy to command their AShMs to deliberately ID and focus on the arsenal ship (given an arsenal ship would very much be a high value target as part of the task force) by having such a small target within the task force that it's difficult to ID and lock onto it in the first place, especially given the layers of hard kill and soft kill measures there would be.
An arsenal ship of course would have a similar vulnerability to submarines as all other surface ships in the task force and the responsibility of ASW would be with the rest of the task force's surface ships, but it's not like the arsenal ship would be somehow more vulnerable to submarines in a tactical sense than surface ships just because of its semi submerged nature. At most, being semi submerged means the arsenal ship will sink faster if it's hit by a torpedo (or even a missile as well) compared to a surface ship, but being semi submerged shouldn't make the arsenal ship any easier to detect, track or engage by submarines compared to other conventional surface ships in the task force.
However, being semi submerged
does make the arsenal ship much harder to detect, track and engage by radar and EO sensors or radar and EO guided weapons, compared to other conventional surface ships in the task force.
I'm also not convinced that PLAN needs such a vessel. If you compare the Chinese case for an "arsenal ship" to the American, two things stick out: that USA is more likely to need and use an arsenal ship, as part of an interventionist global foreign policy that seeks "full spectrum dominance", and secondly that USN already has large numbers of warships with large numbers of VLS cells, plus ten supercarriers which of course are the gold standard in terms of power projection. For USN, an arsenal ship is a niche capability that supports an already very robust array of more flexible, general purpose capabilities. For China, the picture is very different, and I suspect that there is more to be gained by further investment in those more flexible, general purpose capabilities, i.e. large surface combatants, carriers, amphibs, bombers.
To be honest I'm not entirely convinced that the Chinese Navy needs such a vessel either -- as you say, the USN's original idea for it was as part of a desire to have "full spectrum dominance" and such a ship would very much be the icing on top of the rest of the large and impressive cake with many carriers, surface combatants and submarines which make up the bulk of their primary combat force.
If the Chinese Navy really are pursuing such a ship, it may be because they have identified a requirement in their own warfighting strategy that they are seeking a unique solution to, and/or they might be developing such a ship because they too want to seek "full spectrum dominance" and that this semi submersible arsenal ship is merely one part of their overall procurement plans (which we don't know of) and those plans may include a substantial amount of the flexible/conventional forces that you described. So such an arsenal ship may still very much be the icing on the cake for the Chinese Navy as well.