China is socialist. Socialism is serving as the stepping stone on the path from the previous system to full Communism. Socialism serves as an important developmental stage as antagonisms from within (counter-revolutionary forces) and without (imperialist powers) are resolved.

It’s hard to pretend China is in any way communist when they have rampant wealth inequality

First, China does have wealth inequality, but its middling in its severity.

(The key is on the linked Wikipedia page, but darker has higher income inequality).

China has a Gini index of 38.2% in 2019, putting them at 71 out of 168 in national rankings. The USA has a Gini index of 39.4% in 2020, putting them at 107 out of 168. (Lower Gini index, and lower ranking are better). The worst nation, South Africa, has a Gini index of 63.0% as of 2014; the best nation, the Faroe Islands, has a Gini index of 22.71% as of 2018^1.

Moreover, wealth inequality has been decreasing in China for about a decade^2, whereas our point of reference, the USA, has seen its inequality steadily increase over the same time span^3. Wealth inequality is also not unexpected in a rapidly developing economy such as China: initially, as the economy grows, certain people financially benefit more than others and wealth inequality increases; over time as the economic growth stabilizes, and with a concerted effort to combat it, wealth inequality levels out and then decreases, as we see happening. Income inequality is not automatically horrible: careful attention needs to be paid to the bottom of the income rankings; comparatively, high wealth inequality is less of a problem if the bottom is not in poverty than if they are. This ties in to my next point,

the wealthiest run the government.

This is not true at all. Wealth does not buy political power or influence within the CPC (or indeed in the Chinese government overall); nor does having power or influence in the CPC enable one to amass more wealth. Those who are wealthy work with the party, as members, to further the goals of the Party to improve everyone's lives, rather than working selfishly against the party to further their own personal goals. To paraphrase Boer[^4], "The private entrepreneurs have not become a class in itself with associated class consciousness, but many have become CPC members or non-party supporters. The social and cultural assumption is that those that have benefited from wider support must contribute to the well-being of others". That is, those who are wealthy do not get to exert outsized influence by way of being wealthy, and do not sit back and glorify their wealth, but instead work by giving back and improving the well-being of others.

The CPC is extremely developed and works for the people; large companies have branches of the party that help steer them. All enterprises (state-owned, private, or foreign) produce annual "socialist responsibility reports" which guarantee that their actions are not putting profit before the goals of the society as a whole: poverty alleviation, environmental improvement, education, and more.

Socialism (and indeed communism) is a structural form that dictates a government's (and economy's) purpose and its relation to society and its members. The goal of a socialist government is to improve the material and cultural lives of its people. To a Westerner, it seems foreign or fantastical that a country could genuinely operate with this goal in mind, and so people would rather say "it's not real socialism", or say that "because it has some problems, it's all bad", than to acknowledge that no system is perfect and as long as the system works to fix its issues and help its people, it is on the right track.

The OP has a non-nuanced and seemingly uninformed opinion on China as well,

Please remember: China is nominally communist. Functionally, they are capitalists with an usual side of excess infrastructure spending. A strong central government doesn’t make a country communist.

They are not capitalist. Infrastructure spending is also not what determines whether they are capitalist, socialist, or something else. Moreover, nobody is arguing that a strong central government determines whether they are communist or not. To say that China is capitalist is a category error and falls into the trap that dictates that using aspects of a market economy automatically negates socialism and makes a system capitalist. I've written a bit more in depth on it elsewhere, but plenty of sources dive in to why China is indeed socialist and why it is faulty to see them as capitalist. Chapter 5 ("China's Socialist Market Economy and Planned Economy") from Richard Boer's book I've cited above serves as a good overview of why it is a category error to call China capitalist.

[^4]: Socialism with Chinese Characteristics. Boer, Roland.