Socialism is not "no private sector," it's a transitional society between capitalism and communism marked by worker control of the state, and public ownership as the principal aspect of the economy. All apply to China. Regarding prolewiki saying that China isn't socialist, that is outright incorrect. You also lied about the CPC saying that socialism is not the backbone of their economy and their goal for further development, you linked a source stating that the private sector presently plays a large but subordinate part of the economy, which is in line with their analysis that they are in the primary stage of socialism:

Then you compare ratios of private to public, which doesn't actually say anything about which sector holds power. The important factor is controlling the commanding heights and critical sectors, and employing marketization in underdeveloped sectors to facilitate growth. Capital is treated in China like a farmer treats wheat, rather than like an uncontrollable force of nature like it is in the US, because China is socialist.