Helping Ensure Access to Local TeleHealth Act of 2023 or the HEALTH Act of 2023 This bill modifies requirements relating to Medicare coverage of telehealth services, including services that are furnished by federally qualified health centers (FQHCs) and rural health clinics (RHCs). Specifically, the bill expands coverage to include audio-only telehealth services. It also permanently allows FQHCs and RHCs to serve as the distant site (i.e., the location of the health care practitioner) for telehealth services and excludes such services from certain geographic restrictions. Payment must be made in the same manner as for non-telehealth services, rather than in accordance with a separate methodology determined by the Centers for Medicare & Medicaid Services.