The decision seems very well written and is worth at least a skim. The section that answers your question is (f), and starts at the bottom of page 16.

As I read it, the decision says that the State's definitely have the police power to mandate vaccination, and suggests that the federal government lacks this authority under the Commerce Clause (but doesn't directly claim that no other authority exists). The basic claim is that OSHA, given it's current legal authority, lacks the right to regulate "noneconomic nonactivity".