The commerce clause cannot be used to abrogate fundamental individual rights, people are seriously misunderstanding what can be done under that clause. There is a mountain of Supreme Court precedent that covers this explicitly, and the specific case of freedom of travel, and also covers attempts to use regulatory technicalities to do the same. The right of Americans to travel freely absent narrow circumstances requiring due process is settled law at this point. This may be inconvenient for anyone that wants to implement a lockdown but this is well-trod legal territory.

I think people are also conflating what the Federal government can do, which is very little, and what local governments can do, which is considerably more. Broadly speaking, the Federal government operates in an "advise and support" role, the legal authority resides with the States and localities. This is an example of where State sovereignty becomes very obvious. But even with the States exercising their broader powers, they are still restricted from violating fundamental Constitutional rights like freedom of speech, assembly, travel, etc.

Supreme count precedent only matters once a court case makes it to court.

Until then, the President of the United States can make an order, and if it is enforced by local authorities, it's defacto legal for the duration.

Not at all. Violating well-established legal precedent that has already been reviewed by the Supreme Court is an easy basis for the courts to place an immediate injunction of the effects of those orders.

This happens in many other contexts, there is no reason to believe it wouldn't happen here.

There is one big reason why the supreme court wouldn't overrule a quarantine order.

You'd be surprised as to what constitutes interstate commerce. I've seen local criminals brought up on federal Hobbs Act charges for their participation in robbing convenience stores. The prosecutor made sure to note that the store was "known to engage in interstate commerce." Almost any business you can think of engages in interstate commerce. Think about it, where does the stock for the store come from? Where were the registers used to process transactions manufactured? Does the business purchase digital advertising? All of those are interstate commerce.

I'm not surprised, because I'm already aware the umbrella is rather larger than most people would expect. Nevertheless, it simply won't cover everything that we'd need covered from a public health perspective. So what happens here?

That only means the federal government can pass a law about it. It doesn't mean they can pass a law that abrogates other constitutionally-protected rights.