There's no English-language article that can fully capture the system because it's a moving target to begin with, and anything official is vague on purpose (to be fair, much of the legislation in the US is too, except the Constitutional backstop and co-equal judiciary does not exist in China). The official messaging is always targeted and curated with a specific audience in mind and how much truth is contained within varies. The best way to describe it without turning it into an essay is that it's "aspirationally market-driven" system that is not defined by a fixed and consistent ideology but rather the constraints of the capacity of the administrative state to control the parts of the economy that is legible to the state. It's not a free market except for the black market, but the black market is frankly huge if nothing else to compensate for the state asserting not just a monopoly on the use of violence but also the monopolistic determinator of morality, which the people are less willing to buy into, but that disconnection itself creates an opportunity for arbitrage. That is the relationship dynamic that have retained some degree of stability, but everything else is effectively subject to change on a dime without notice. The party will never accept openly that it is capitalistic and in some sense that's not even a lie, but what the state is able to impose and what the people actually do are very different things. As the state excludes 99% of the population writ large from politics, full stop (you are either born into it, or you're not eligible to participate, with some narrow exceptions that occasionally pop up), there's not much of a ground-level appetite for dogma and doctrines. Instead you end up with a pragmatic, descriptive market that exists differently within and without, and just like the socialism label being basically symbolic, same goes for capitalism.
People have been talking about late capitalism in the west for a century. The Chinese state would argue that we cannot be in late capitalism because we're actually in the first stage of socialism, and the people would wonder how we got to late capitalism when they never got to experience early or middle capitalism. But really the only thing we know that definitively does not work is implenting Marxism and Marxism-Leninism and Maoism and its offshoots as doctrine. Whether that means that the default is a prescriptive version of capitalism is, well, open to debate, and probably too simplistic.