Cuba, USSR, Vietnam, etc. Socialism works.

China 100% counts as socialist. The Gang of Four diverged from Marxism-Leninism into ultraleft dogmatism. Ultraleftism is not "pure socialism," there is no such thing as "pure" socialism, capitalism, etc. The PRC under Mao had markets, private property, etc, as did the USSR. As a consequence, the modern CPC is course-corrected to a standard Marxist-Leninist outlook. Both Mao and Stalin are seen as 70% good by the modern CPC.

The claims of "authoritarianism" are the repression of capitalists.

Yes, I've read Capital, volume 1. I'm on volume 2 right now. More importantly, I've read a ton of Marx, Engels, Lenin, and far more Marxist authors, all who speak about Dialectical Materialism and socialism, how to bring about communism, and more, all of which you won't find in Capital. I'm skeptical that you've even read Volume 1, to be honest, your understanding of Marxism is incredibly poor. Using "I've read Capital" as an "I win the argument" tool is incredibly poor rhetoric, if you have a good argument, make it, don't appeal to your own authority.

Yes, political theory isn't a religion, you seem to think it is though.