How much does state health insurance cover for therapy and psychiatry visits? Does it differ state by state?

Yes - Varies. This will vary from state to state. You will want to get a phone number or web site that you can use to check benefit.
State health coverag. This definitely varies from state to state . With health care is supposed to have parity with other medical disorders. Medicaid is state regulated. Medicare now pays about $50 per session .
Coverage. Covers most of expenses and differs from state to state.
Varies. States vary in what they pay for services under medicaid. In a recent article in forbes, medicaid payment for general medical services were compared to medicare (federal) payment. The range went from 29% in ny to 113% in alaska. States vary in what specific services they cover as well.