Is China communist or capitalist or, somehow, both

As China embarks on a "New Era" and officially adopts "Xi Jinping Thought on Socialism with Chinese Characteristics" (thus raising President Xi, the current leader of the ruling Chinese Communist Party, to Mao-esque almost god-like status), the question arises: in what respect can modern China be considered socialist or communist?
Under Chairman Mao, the state (i.e the Chinese Communist Party) owned every factory and every farm in the country, and the means of production was effectively collectively owned. Since 1976, though, China has all but abandoned the tenets of classical communism, and now just about everything is at least partly privatized, leaving a patchwork of public and private businesses, not dissimilar to many other mixed economies across the world. Even schools maybe either state-run or private, and its tax codes and rates are similar to those in the USA and elsewhere.
Mr. Xi's predecessor Deng Xiaoping, once one of Mao' top generals, is generally credited as the propelling force behind China's move towards capitalism, decentralization and market economics. He was quite up-front about the need for China to reform its economic systems in order to "catch up with the times".
Yes, all the land in China still technically belongs to he government, the banks are government-owned and -run, and the domestic media is all state-owned and tightly controlled. Furthermore, the country and its provinces still operate under the highly-centralized single-party rule of the Communist Party, and all government employees must be Communist Party members. Many of China's largest amd most successful companies are state-owned, and even many successful private companies have "links" with the government, some more transparent, some less.
But economic policy is now very much geared geared towards capitalistic ends. Regional leaders are evaluated each year based on the region's economic growth, and fierce competition is encouraged (with concomitant high levels of corruption).
Internationally, the country is even more capitalistic in its outlook. It now has the second-highest GDP in the world, and will probably be the world's largest single market economy by 2050 (it may already be by some measures). It has opened up to capital investment, and has a sophisticated stock exchange and capital markets. Not a day goes by without more news of aggressive international corporate takeovers. Since the advent of Donald Trump in America, China is the de facto leader of globalization and the official poster-child of free trade.
Even though China's government is officially Communist, it's people have most definitely embraced capitalism. In a recent Pew Research Center study, 76% of Chinese people agree that "most people are better off in a free market economy, even though somepeople are rich and some are poor" (this compares to 73% in Germany, 70% in the USA, 65% in the UK, and a 64% global median).
Today, China is neither a communist country with a veneer of market economics, Perhaps China's economic system might best be described as state capitalism, a combination of capitalism with state control and ownership, where the government controls the economy and essentially operates like a single huge corporation. China's continued use of terms like "socialism" and "communism" are really inaccurate anachronisms. They are slightly more palatable than words like "totalitarianism", but they are also a million miles from the purist vision of Karl Marx (or even Mao Zedong).