9/11 Responder and Survivor Health Funding Correction Act of 2023 This bill modifies the funding of, expands eligibility for, and makes other changes to the World Trade Center Health Program. This program provides medical monitoring and treatment to responders and survivors who suffer from health conditions related to the terrorist attacks on September 11, 2001. Specifically, the bill provides additional funding for the program through FY2033 to cover program costs. It also sets out a new formula to determine funding amounts for the program from FY2034 through FY2090. Additionally, the bill expands eligibility for the program to include members of the Armed Forces and federal employees and contractors who provided rescue, recovery, demolition, debris clean-up, or related services in response to the attacks at the Pentagon and in Shanksville, PA on September 11, 2001. The bill limits the enrollment of newly eligible individuals in the program to 500 at any given time. Other changes in the bill include (1) allowing certain health care providers other than physicians to determine whether an individual's health condition is related to an attack, and (2) making the program administrator (rather than the centers that collect and analyze health data generated from the program) responsible for establishing criteria for credentialing health care providers that participate in the program.