Supporting the Mental Health of Educators and Staff Act of 2023 This bill establishes grants and requires other activities to improve mental and behavioral health among education professionals and other school staff. Specifically, the Department of Health and Human Services (HHS) must award grants or contracts to educational agencies, institutions of higher education, or consortia of such entities for programs to promote mental health and resiliency among education professionals and other school staff. In addition, HHS may award grants for educator preparation programs and training. Additionally, HHS must conduct a campaign to (1) encourage education professionals and other school staff to seek support and treatment for mental and behavioral health concerns, and (2) disseminate best practices to prevent suicide and improve mental health and resiliency among education professionals and other school staff. HHS must also study and develop policy recommendations on improving mental and behavioral health among education professionals and other school staff, removing barriers to accessing care and treatment, and identifying strategies to promote resiliency. Furthermore, the Government Accountability Office must report on the extent to which relevant federal grant programs address the prevalence and severity of mental health conditions and substance use disorders among education professionals and other school staff.