This, naturally, extends to the federal government
It definitely does not naturally extend to the federal government and they will have to make a much more convincing argument on why it should.
Why not?
It is the duty of the federal government to ensure life, liberty, and the pursuit of happiness is not invalidated. And if a state has the power to ensure that the public is protected and healthy from a disease, then the federal government, which must manage trade and travel between states, can ensure the same as all states have interstate travel and trade.
This is how they are doing it with OSHA. Essentially stating that a business of 100 people will have interstate commerce and thus must provide a safe workspace that will ensure that any disease is not transferred to other states.
I mean, Biden could just ban interstate travel if vaccines aren't a thing. But... This seems like a better choice.