2k-year-old wine and the uncanny immediacy of the past

I don't think anyone knows enough about the period to answer that question. Our main written source is the Annals of Spring and Autumn (春秋), from Lu (not Yue https://en.wikipedia.org/wiki/Yue_(state)) which spends 18000 words on 242 years, in chronological order. For many of those years it simply says something like "螽" ("locusts"). It does not go into any detail on questions like which hobbies the kings of other countries spent their spare time on, and that's a difficult thing to infer from archaeological evidence, too. The written records of Yue were destroyed by order of 秦始皇 in the 焚書坑儒.

So we kind of have to guess. My guesses are not the most informed.

The sword (https://en.wikipedia.org/wiki/Sword_of_Goujian) is bronze, so it was probably cast (you can forge bronze but the cost/benefit ratio is terrible). You could imagine a king pouring the hot bronze into the mold—that would be much quicker than forging an iron sword—but you probably wouldn't want him to make a habit of it, because contaminants in the metals would expose him to arsenic vapor, though this sword in particular is almost arsenic-free.

Then all that's left is sharpening the blade, which any warrior has to be good at, and what is a king if not a warrior foremost? So it's plausible that a king might have put in most of the work embodied in the blade himself, with a grindstone, even if he didn't go around casting bronze regularly.