Your knowledge of US Constitutional case law seems a bit lacking.
States can compel vaccination. This was settled by the SCOTUS over a century ago. Jacobson v. Massachusetts, in which Jacobson tried to argue that compulsory vaccination (against smallpox, in 1904) was unconstitutional, and the court found that, in the interest of public health, the states have the right to compel vaccination.
From that decision:
"...in every well ordered society charged with the duty of conserving the safety of its members the rights of the individual in respect of his liberty may at times, under the pressure of great dangers, be subjected to such restraint, to be enforced by reasonable regulations, as the safety of the general public may demand"
"...[r]eal liberty for all could not exist under the operation of a principle which recognizes the right of each individual person to use his own [liberty], whether in respect of his person or his property, regardless of the injury that may be done to others."
This precedent already justifies the mask mandates, enforced business closings, and other pandemic control efforts. It has been referenced over and over since 1904 (like, in the 1918 flu pandemic, etc). This is pretty solid precedent, and why the courts have roundly rejected challenges to the various state measures already in place.
The problems facing compulsory vaccination in the US are not legal, but political.