> can they knowingly allow their child to do something harmful and then sue because it turned out poorly
That likely depends on how that "something" was publicly marketed to both parents and children based on the company's available information. Our laws historically regulate substances (and their delivery mechanisms) which may lead to addition or are very easy to misuse in a way which leads to permanent harm (see: virtually all mind-altering substances); even nicotine gum is age-restricted like tobacco products. Because nicotine is generally considered an addictive substance, it's regulated, but few reasonable people would argue that parents should be allowed to buy their children nicotine gum so their kids calm down.
Consider how, decades ago, the tobacco companies were implicated in suppressing research demonstrating that tobacco products are harmful to human health. The key here will be if ByteDance has done the same thing.
Also, to play off your point on cheeseburgers: remember the nutritional quality of one cheeseburger versus another will vary. If made with top-quality ingredients (minimally-processed ingredients, organic vegetables, grass-fed beef, etc.), a cheeseburger is actually quite nutritious. However, in a hypothetical situation where a fast-food chain was making false public claims about the composition of their cheeseburgers (e.g., lying about gluten-free buns or organic ingredient status), and someone is harmed as a consequence, the victim might have standing to sue the fast food chain.