Communism

I'm not trying to argue with you, just see more where you're coming from, what your present understanding of socialism and China in particular is, etc, so that I can help bridge the gap. For clarity, I'm a Marxist-Leninist, I study theory and organize in real life (though less than I'd like to admit, which is something I'm working on).

The PRC does mass produce a huge portion of the world's goods, yes. This alone isn't incompatible with either capitalism or socialism. China has a private sector, largely relegated to small/medium firms, and secondary, ie not critical or key industries. The public sector governs the large firms and key industries, including finance.

Even checking Wikipedia, data from 2022 shows that the overwhelming majority of the top companies are publicly owned SOEs. This is China's strategy, they've been honest about it from the beginning. The private sector is about half cooperatives like Huawei or farming cooperarives and sole proprietorships, with the other half being small and medium firms. As these grow, they are folded into the public sector gradually. This is China's Socialist Market Economy.

China's relation with the world market came into being as a result of Reform & Opening Up, which agreed to foreign investment as long as the PRC retained sovereignty over the invested capital, and technology and knowledge transfer was mandatory. This is the secret to stablizing their growth, which was positive but unstable under Mao and the Gang of Four, as the PRC was developing from a largely agrarian economy to an industrialized one:

Class struggle does continue in socialism. The idea that it ends is one of the reasons the USSR liberalized towards the end and dissolved. China's market reforms were made not with blindness to their danger, but with control and containment, often described as a "birdcage model." In this way, the proletariant retains dominance over the state and the commanding heights of industry, while capitalists largely exist purely to facilitate the beneficial aspects of markets, such as rapid development of underdeveloped industry. As these firms grow, they are folded and integrated more into the public sector.

As for the state being run by the working classes, this is also pretty straightforward. Public ownership is the principle aspect of the economy, and the CPC, a working class party, dominates the state. At a democratic level, local elections are direct, while higher levels are elected by lower rungs. At the top, constant opinion gathering and polling occurs, gathering public opinion, driving gradual change. This system is better elaborated on in Professor Roland Boer's Socialism in Power: On the History and Theory of Socialist Governance, and we can see the class breakdown of the top of the government itself:

Overall, this system has resulted in over 90% of the population approving the government, which is shown to be consistent and accurate. If you want to learn more Roland Boer also has a good book called Socialism with Chinese Characteristics: A Guide for Foreigners, which is more specifically about the PRC and goes beyond the structures of governance to the more broad system of socialism in China. While not nearly as in-depth due to time limits as Roland Boer's work (and mostly focused on the Xi Jinping era), Red Pen's A Summary of Xi Jinping's Governance of China can be a good primer! There's also This is how China's economic model works: Explaining Socialism with Chinese Characteristics by Geopolitical Economy Report.