Due process is a bedrock of American law. It means government officials can't just "do what they want" and make arbitrary decisions with specific targets -- which is exactly what the TikTok ban is.
You want to ban TikTok? Great, you need a specific law from Congress that outlines under what circumstances companies may be banned in the US, and then prove the specific company meets those standards.
None of that has been done here. The president is not a dictator. TikTok should absolutely sue.
Note: this is regardless of anything TikTok has actually done privacy- or security-wise. The point isn't whether they're dangerous, the point is whether we can meet some standard of showing that they're dangerous. If they're dangerous, we need to establish how and why legally. This is what separates the rule of law from dictatorship.