I'm guessing this is a lot harder to stop than a drone though. If you're getting a slug of solid metal coming at you at hypersonic speeds, presumably destroying or deflecting it is a non trivial problem. And I'm guessing this kind of weapons would be mounted on ships with nuclear reactors?
With respect, I think that taking lessons in naval warfare from ground warfare is a bit questionable.
Due to the ranges involved naval warfare, drones of sufficient range and power and communications capability are already going to be much larger and more expensive than your average ground combat drone. Not only that, but they have to carry much larger payloads to reliably take out a ship, and they have to be fast and evasive enough to be reasonably capable of penetrating the layered defences of a naval battlegroup when massed. Not only that, but naval drones have to be navalized (made resistant to salt water spray, collapsible wings for storage, etc) and launch platforms are expensive ships, not cheap patches of dirt.
None of the above are problems for ground combat, which makes ground combat suicide drones much cheaper to produce and field in numbers. If you look at current prototypes for naval strike drones, they mostly look like slightly smaller jet fighters instead of much smaller ground combat drones.
Well like you say, we don't have any insight into the PLAN planning or R&D projects. From the information we do have, the Type 055 Destroyer has an integrated power system that some articles have mooted to be laying the groundwork for a future railgun system. It's possible that the PLAN has also made some sort of breakthrough (or is close to doing so) with the power miniaturization or storage systems that would be necessary to fit one onto a Type 055. Either that, or the PLAN is doing this as a vanity project, which is pretty out of character for them.
As for hypersonics, naval missiles are housed in VLS silos that can't be reloaded at sea. Even if the mooted railgun can only fire a few dozen or so shots before requiring a barrel replacement, that still works out favorably if the barrel replacement can be done at sea. Also consider that it's possible that hypersonic missiles might still be impacted by jamming or some future interception system, whereas a metal slug travelling a mach 3 tends to not care about either. As for a sub surface nuke, setting aside the very obvious environmental damage (China plans to fight near it's home waters so can't be so blase about nuclear contamination), using any sort of nuclear weapon is a huge step up the escalation ladder and would be only one step down from striking a US base with nukes.
I'm not an expert on this stuff either obviously, so I'm just speculating on the benefits China might see in is pursuing this. It's worth noting that these things aren't mutually exclusive. I can see how this could be used for specific situations while drones are used as a more general type of weapon. Kind of how Russia uses hypersonics for some pinpoint strikes on high value targets.
I figure there is a reason they're pursuing this, but could also be a moonshot project where they don't necessarily expect it to become practical, but want to see how far they can push it. As you said, they're bound to discover some new tech through this process so even if the particular application doesn't pan out, it's not a waste of time to understand this stuff.
The goals are a bit different though. The problem with plasma containment in fusion reactors is that plasma moves in unpredictable ways, and the amount of energy you need for a reliable containment field is higher than the energy output of the reactor. For this sort of application you'd be using the field for a containment of a metal slug and it just means eating more power. Regarding the power issue, it's worth noting that it would likely use supercapacitors. So you don't necessarily need a powerplant that can output 25 MW directly. You'd just charge up the capacitors for a few shots.
And yeah, it looks like China's taking a very broad approach to tech development. This sort of system could potentially be used for launching small satellites as well.