Does OSHA have it’s own special police force to make sure that “No state leaves OSHA without OSHA agreement and approval to do so”?
Not that I know of. There may be an occassional visit to make sure the state inspectors are competent, but i don;t think even THAT is done.
States and feds mostly cooperate to control the public, and workplace safety is one of those places where government interests tend to align without much contention.