State capitalist is a fine description so long as one understands that to mean it's a transitional system. Socialism can only be fully acheived (marked by the abolition of class) at an international scale, but a workers' state can be established in individual countries and develop the forces of production there in the mean time. This not only serves the purpose of internationally demonstrating the superior suitability of the workers as a ruling class compared to the bourgeoisie, but builds the necessary material conditions that gives rise to full socialism. The official CPC theory is that China is on the socialist road guided by the whole process people's democracy. They're 2035 goal is to basically realize socialist modernization, and by 2049 to be a great modern socialist country.

One way to think about it is that China has a bourgeoisie the same way Great Britain had a monarch and aristocracy in the 19th century: the old ruling class is deliberately propped up to the rest of the world for appearance's sake, but their power has been hollowed out to the point that they're mere figureheads who provide cover to the actual ruling class that would otherwise be treated with extreme suspicion & hostility. China's bourgeoisie face many restrictions on investing capital, liquidating capital, operating a business, setting prices, and are broadly subject to have their assets taken by the state for any number of reasons. Of course, they're still able to become immensely wealthy and live in luxury, but they face significant scrutiny and are culturally encouraged to live quiet lives. This enables the PRC to operate a market economy that on the whole functions dramatically better than market economies operated by a bourgeois ruling class, and that's before you consider the large share of their economy that is directly controlled by the state and the central planning apparatus that reigns over the entire economy. It's a truly impressive system (granted, all centrally-planned systems are impressive relative to capitalist systems), and perhaps their greatest stroke of genius was taking advantage of cold war geopolitics to become the cornerstone of the global economy.

And what's so cool is that this is just a peak at what international proletarian rule could accomplish to bring about full socialism and the abolition of class.