Even the old USSR in their prime did not have such a robust carrier program and they spent a much much higher percentage of their GdP on their Navy than China does.
Not want to diminish china´s Carrier program, but the in the decade of 80´s, USSR did have a far more robust carrier program than china has today. Fom 1982 to 1988 they started construction of 3 large carriers (including a nuclear supercarrier with catapults). The soviet naval aviation center, NIKTA, (in presente day ukraine) AFAIK is equipped with catapult.
China still hasnt started construction of any carrier, and although it most certainly has a catapult program, we have seen little signs of it, or how advanced it is.
Of course, as you said, USSR spent a much higher percentage of GDP on the military than china and they had decades of heavy industry advance. And that contributed decisively for USSR bankrupcy, something that the chinese leaders know very well.
I have little doubt that with time and resources (that does china have), it will indeed have the second largest carrier force in the world. I think its a matter of when, not if. But in the short/médium term, it still cant achieve what USSR did in the 80´s.