You should really actually watch the episode. It's a blatant dig at China's government, censorship policies, and treatment of political prisoners. Its treatment of `China invading the US` were not out of `paranoia`, as you say, but based out of reality. It attacks Disney for making similar concessions to the Chinese government in its MCU movies.
Spoilers, but deeper analysis:
Randy's story arc this season appears to revolve around surrendering your morals for the next dollar- for example, last season he turned down a deal with a large marijuana corporation to continue his home-grow operation, but proceeded to create a partnership with them in the season premiere to ensure his stake in South Park's weed market. The scene where he garrotes Winnie the Pooh in this episode, to me, is an extension of this same theme- the sellout of what we've taken as sacred, except now, it's to China's CCP. Contrast that to the name of Randy's farm, which is a bastardization of the word `integrity`.
The entire segment about the band biopic in this episode is basically saying the same thing but far more overtly.
Or... the portrayal isn't actually targeting group of the character embodying the trope. It's targeting those that hold such tropes, in a way that exposes the absurdity of them.
There was a movie few years ago, Tropic Thunder. Robert Downy Jr is in black-face the entire movie, and it's hilarious - and somehow he isn't cancelled. Why? His character in the movie is a white, self-serious method actor (he stays in character all the time), who had medical treatments to alter the pigment of his skin in order to portray the African-American lead in a movie. And his depiction is one giant super charged trope. But the actual butt of the joke isn't black people - its actually the pretentious actors and Hollywood in general. In essence, its making a statement about the absurdity, self-importance, actors, studios, etc in Hollywood, and the lack of the social justice and equality there.
South Park wields "*ist" tropes in a similar way, and I think its incorrect to think of it as racism, or xenophobia, etc.
In South Park, there's one black character in the cast, and his name is Token. As in the token black kid. Out of context, and on its face, it might seem racist. But its saying something else, just like RDJ's role in Tropic Thunder.
Thank you, it just clicked...
My model of the Chinese government at the moment is that they primarily care about opposition/disrespect/criticism of the Chinese government. Does anyone have data points as to whether they care about, say, present-day racist insults of (a) Chinese-Americans; (b) Chinese living in China? Might be interesting to see where the lines are drawn.