Edit: I stand corrected, they are bound by our laws, but it's orders of magnitude easier to enforce those laws on a company based in the US than a company based in China.
This is how EU rules apply to US tech companies. US rules for Chinese tech companies is no different in principle.
IMO however the problem isn't privacy, it's being able to stick a thumb on the algorithmic feed and control the information consumption of a slice of society. And TikTok isn't the only problem, it's broadly applicable across consumer tech.
Theoretically, yes. But the US isn't a police state where their activities would be constantly monitored in great detail for compliance. There's a lot they could do under the radar, and a lot of groundwork they could lay for some future inappropriate action.