I don't think China cares much about starting an arms race because, let's be honest, nobody is even remotely close to China's pre-arms race capacity to even try keeping up if China do choose to ramp up.Carriers by themselves(nuclear or no), especially if produced in series(important), aren't that expensive.
Their stretched production (when there are effectively no two similar ships) with concurrent endless RND is what makes them ridiculously expensive.
In principle, launching 3 pairs over 9 years is possible and within what we saw about previous times China activated macro 3d printing.
It isn't as much a technological/financial challenge IMHO as it is an obvious bet to "rule the world", invitation to prewar naval arms race in purest terms.
IMO China simply don't consider carriers to be as critical to its doctrine and strategic planning. I think because US doctrine revolves around carriers and made it a symbol of their naval power, a lot of people ends up look at carriers more as a symbol than for its utility.
But even ignoring all the analysis, we can already see from Iran war that carriers' offensive capacity in the age of missiles and drones is a lot smaller than 30+ years ago while their vulnerability became much larger.
They still have enormous utility in achieving local air dominance, providing defensive fighter screen against incoming aerial threats and in some instances anti shipping, but unless you're bombing civilians, the role of offensive strikes against real militarizes are mainly the job of drones and missiles. As such you don't really need as many carriers as force design based on using carriers for air to ground strikes.
I think the fact that China built Type 076 and are investing heavily in drone strike platforms basically corroborate this theory and explains why China isn't rushing to build more supercarriers, even though it can easily do so.
And I think the reason western analysists would give wild predictions on China's carrier count is because they're applying US naval force design on their assumed Chinese strategic objectives.