I'm not sure that a foreign company has any rights under the constitution to begin with. It's contentious whether or not it grants rights to a foreign citizen while they are outside of the US's borders, so claiming that ByteDance would have their constitutional rights violated by such a ban would be even more so.

However, if this were to happen, it would almost certainly be under national security law, which has pretty far reaching powers for this sort of thing. Knowing how much the app spies on you, and knowing that they are ultimately under control by the Chinese government, there's a very strong case to be made.