they'd need something like the Glomar Explorer to assemble it properly
I think it's going to be more like an oil rig that's built on shore, floated/towed out to its destination, then sunk in place. It's too big to do much assembly underwater. The story says it will "host dozens of people for up to a month".
The pressures at those depths are immense. It can actually affect the structure of alloys at the molecular level. If you don't use the right one, or the quality control is off just a tiny bit, and you're in trouble.
It's not that exotic anymore, people have been building deep sea submersibles for quite a while. Heck, even James Cameron was able to build one that could descend far deeper than what the Chinese intend. China's resources are far in excess of what was available to Cameron. Not to mention, China already owns submersibles that go down twice as deep as this lab.
The challenge of this lab is that it would be immense. Instead of building a 6 foot sphere, you're building 20 foot spheres, and connecting them to each other. The materials technology is already there, it's the engineering problem of scaling up the machines that grind/shape the metal.
I'm guessing it could easily cost a billion dollars, but then again, last year they spent $216 billion on R&D. I dunno what kind of ROI they expect to get, but the fact is that 70% of the earth's surface is underwater and there's plenty of resources down there for the taking. We don't have the technology to harvest most of them yet, but maybe they don't expect any immediate return, maybe they're taking the long term view.