The Chinese government and the US government exert their influence over companies in the same way -- regulation, backdoor conversations asking them to kill/mute stories, and NSL type requests. There's not some government propagandist sitting at a switchboard. In fact it's the "West" that goes above and beyond with an entire technical apparatus to real-time mass censor social media to "protect democracy." If you don't consider every US company to be a direct arm of the US government but do for China then it's because your feeling about China than your feelings about social media manipulation.
It is in China's interest to avoid divestment because TikTok is a successful company making China money. And now it's in their interest to avoid divestment to not get bullied by the US gov't. If TikTok had the power you and others in this thread ascribe to them they would be more successful at swaying public opinion.
I do. I live in the EU, and our laws arguably don't allow sharing data with US companies for that exact reason (Schrems II judgement)
It doesn't matter why TikTok does anything. They have shown they can influence their users en masse, and they're legally obligated to do it if the Chinese authorities demand it.