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.
(Yes, I know this is a company owned by the Beijing based ByteDance but that’s not immediately disqualifying of this US corporation run under US law being able to defend itself in a US court system as any other US company would.)
It's not immediately disqualifying, no, but it would almost certainly be squashed quite quickly by the US's NSL. (Funny how the NSL in HK and the US are both so pertinent in China related discussions these past few days!)
Having set up a corporation on US soil does not grant free pass to a foreign government to spy on US citizens.
I would think it's actually Google and Apple's constitutional rights that would be at issue, since they're the ones hypothetically being restrained from publishing certain apps.
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.