if I have some previously unexamined belief that's rooted in racism, I do earnestly want to correct it.
I already pointed them out and you doubled down, but I'll try to give a quick explanation.
The PRC is socialist and governed by a communist party. They have a series of 5 year plans that culminate in reaching full socialism by 2050.
The reason many westerners say they're "communist in name only" is partially because of the reforms under Deng that allowed for capital development in order to build the productive forces that could be utilized to build functioning socislism under the nose of US imperial hegemony. Those reforms were controversial amoung communists at the time, but the government under Xi is making good on the intention of those reforms right now, and history has proven them to have been effective. The other part of the reason is Western chauvanism/rascism. "Non-whites cant do socialism right - they're authoritarians." This arguement is leveled at every actually existing socialist project by Western "leftists."
So it isn't "nonsensical" to consider the PRC to be what it considers itself to be, and has demonstrated itself to be. You just have to actually be informed about it
The original point about "can't do socialism because of large, heterogenous population." Besides being obvioulsy wrong because there's examples of actually existing socialism that had or have large, heterogenous populations, i always point out that the statement is rascist. I do this because most people repeating it, haven't even thought about how its rascist.
Its a brainworm people in the US use to explain why they can't have the kind of social democracy they have in Scandinavian countries - at least that's the context I've always heard it used. This is a "nonsensical" trueism. First, the Scandinavian countries they're refering to are 1) not socialist to begin with, they're social democracies. 2) they aren't homogeneous, they also have ethnic minorities and have rascism.
That statement is not a meaningful acknowledgement of rascism, its an acquiescence to it. Its an appeal to rascism as an arguement why something just can't happen in the US. It also ignores the actual reasons impeding social democracy, let alone socislism which is the entrenched position of capitalist hegemony, the power and depth of its propaganda apparatus, and the relatively privileged position of US workers vs those in the global south due to imperialist exploitation and extraction.