So where in the constitution does it state that the federal government cannot mandate vaccines?
The Federal Government only has powers that are specifically delineated by the Constitution.
There is nothing in the Constitution that gives the Feds the power to mandate vaccines, therefore, they can't.
If it seems that the Feds have total autocratic powers... it's because of creeping Federalism in which the interpretation of the powers given to the Feds continually gets broadened.
*A lot* of Federal regulation, e.g., is based on the Commerce Clause (if it happens across state lines, the Feds are in control). All three branches have wittingly or unwittingly given themselves and the other branches more and more power. Also, international issues (like wars) tend to favor giving the Feds more and more power. And Congress has been reluctant to reign in Executive power for decades, or, not providing the legislation needed in new situations, forcing the Chief Executive (and all the Federal Agencies) to make up their own rules.
However, this isn't entirely unchecked. The courts do regularly slap down Congressional or Executive overreach (at times expanding their own powers to do so).
Anyhoo... getting back to what the Feds can do with regard to vaccine mandates... they can't.
States have all the power that the Constitution hasn't relegated to Congress or limited through delineating the rights of individuals. There is no Constitutional right to be free from enforced vaccinations. So... the states can do that. And if we don't like that... there's the voting booth.