but a PWA wouldn't stop this. Most of the mobile APIs aren't available on PWA and if the site is blocked via route it won't help
Being ignorant of the special area of law that is “Presidential emergency powers regarding trade with foreign nations” isn't necessarily being really weak on US law generally, though that narrow area of law ends up contravening a lot of what you might correctly understand elsewhere when it is triggered.
It's not clear exactly what the content of the order will be, without which we can't really begin to assess whether he has the power to issue it, but there are certainly, at a minimum, things he could due to obstruct their ability to fully interact with US markets under Presidential emergency powers. Given that Trump's I formal descriptions preceding executive actions have not been a particularly good guide to the details of the actions, I don't know that any deeper analysis wouldn't largely wasted.
I'm a huge proponent of regulating big tech companies, but all regulation needs to done under the framework of public and universal rules established in advance, not randomly banning individual apps without proof of wrongdoing or a way to mount a defense.
If TikTok is doing something bad, fine. Make a rule against the bad thing, then ban TikTok on the basis of breaking that rule. You can't just bypass the whole "make a rule" and "show that $X broke the rule" thing and go straight to "punish X". That's called passing a "bill of attainder", and it's such a terrible idea that the practice is specifically banned in the constitution. Now, maybe this situation isn't technically a bill of attainder, but it's the same damned principle at work, and it's still a bad idea.
[1] https://www.eff.org/deeplinks/2015/04/remembering-case-estab...
Yes, as long as the punishment isn't essentially criminal in nature, you can, and it's long been a regularly used tool of foreign policy, under the International Emergency Economic Powers Act. When sanctions are declared against foreign companies or individuals or trade with them otherwise restricted, it's based on declared threats to the country, not general rules that are announced in advance and then the specific individuals involved found guilty in some judicial process of breaking after the rule was declared. It's all by executive finding.
The state absolutely can order parties not to participate in any way with trade prohibited under it's Constitutional power to regulate international trade.
Which includes Presidential directives issued under the International Emergency Economic Powers Act.
He's not talking about banning the TikTok app narrowly, but banning TikTok from operating in the USA (which, assuming he's acting under the International Emergency Economic Powers Act, could also including either preventing or directing and compelling sale, transfer, etc., of any of their property — or any property in which any foreign person holds an interest.)