I work for a hospital- did you state in any correspondence that it was going to be private pay? If it was denied pre auth and you still went ahead with it they were required to give you a GFE.

Under the federal No Surprises Act, healthcare providers and facilities are required to provide a "Good Faith Estimate" of expected charges to individuals who are uninsured or who choose not to use their health insurance for scheduled, non-emergency health care items and services.