Veterans' Health Empowerment, Access, Leadership, and Transparency for our Heroes (HEALTH) Act of 2023 This bill modifies the Veterans Community Care Program (VCCP), including by requiring the Department of Veterans Affairs (VA) to develop and implement plans to improve the administration of the VCCP. Specifically, the bill provides statutory authority for the VCCP eligibility standards for when a veteran is eligible to elect to receive non-VA care through the VCCP. The VA must notify a covered veteran of eligibility for care or services under the VCCP within two business days after the VA is aware the veteran is seeking care. If a request by a veteran for care or services under the VCCP is denied, the VA must notify the veteran within two business days of the reason for the denial and instructions on how to appeal the denial using the clinical appeals process of the Veterans Health Administration. Among other elements, the bill also requires the Government Accountability Office to report on the VA's efforts to ensure veterans are informed about eligibility for care and services under the VCCP and the performance of the Office of Integrated Veteran Care in improving access to care for veterans in VA facilities; VCCP providers to submit a claim for payment to the VA not later than one year after the care or service was furnished (current law requires submission within 180 days); the Office of Inspector General of the VA to assess the performance of each VA medical center in implementing the VCCP.