But, the bill of rights doesn't just address the powers of the people, it restricts the government. Thus, you could read as much from it's omission as a right of the people as you could it's omission as a power of the federal government.
The 10th amendment would seem to allow individual states to enforce vaccinations, limited of course by their own state constitutions.
Did I miss the memo where Fauci was given emergency powers? Because the executive orders came from Biden for federal employees and medical workers. And the 5th circuit court (I think) blocked the OSHA requirement. Which is our three branches balancing each other, as intended.
I guess next move of Biden: does he go at it differently? Does he push Congress to enact something, what?
Personally, I would have OSHA push the current standard as a non regulatory recommendation. That would give employer's flexibility to whether they are following this standard, or not.