The issue is the fact that Chinese companies have dramatically better access to the US market than American firms have access to the Chinese market. This is a regulatory and trade failure of extreme incompetence that has never been properly addressed by Congress or the President.
If Facebook, X, Pinterest, Reddit, et al. can't exist freely in China, then TikTok doesn't get access to the US (until ByteDance becomes a minority shareholder etc).
TikTok follows US law. The companies you mentioned exited China because they didn't want to build out their own part of the Great Firewall. The irony in this criticism is that the US companies were mostly responding to domestic political pressure not to abet Chinese censorship. So it was more like export controls that caused the exodus of US companies rather than import controls.
In the old broadcast media days, US kept a pretty close eye on foreign media networks and they never had a foothold the way American media companies had. Think RT
Meanwhile, VOA operated (still does) around the globe spreading freedom and liberty. (Not sarcasm, really...)
Today, we have foreign media operators serving content to the American population, including minors, unfettered.
Look at the disasters of the 20th century for evidence of the power of ideas. A group of people united by an idea is a force to reckon with, and we're allowing foreign agents to control the flow of ideas on a broad scale. (I'm not against free speech, quite the opposite, I'm just pointing out the obvious).
These questions aren't simple to answer, nor are the proposed solutions going to make people happy, but you've rightly identified they're of pressing national concern.
One thing is for certain: we're in for the time of our lives.
Even if you assume there's some magic subliminial Sinocentric messaging in the app, by the time the TikTok audience is old enough to be in positions of power, its influence will be long gone-- a stock photo screenshot on a nostalgia slideshow next to "remember the Xbox 360?" or "That white second-generation Prius that there was one of in every neighbourhood." This will all blow over in another few years. The kids will move on to VipVorp and Slipppper, parents' groups will while about the scourge of four-dimensional VR hyper-porn, and the world will keep spinning.
If the rise of China is an actual existential threat (spoiler: it's not-- there's a difference between "we can't act with complete impunity on the global stage anymore" and "suddenly we have the per-capita GDP of Haiti") then it's going to take more than economic roadblocks and scare tactics. America has to make itself more competitive-- better education, better infrastructure, more strategic use of subsidy and planning tools, more money in R&D and less on stock buybacks.
You basically can't operate in China without somehow letting the CCP in on your affairs. A great example is the automotive industry: American car companies had to work with Chinese-based counterparts in joint ventures to have any operations in China prior to 2017. Microsoft had to let Chinese officials look over the Windows source code to get it approved for sale in PRC. Hollywood routinely modifies movie productions to appeal to Chinese censors and audiences, even at points in the production where the changes would impact the release outside of China (see the remake of Red Dawn). American companies do this because they fear losing access to the market; Chinese companies do not have to do the same for access to the American market.