Health Care for Homeless Veterans Act This bill extends authorization through FY2029 for the Department of Veterans Affairs (VA) Health Care for Homeless Veterans (HCHV) program. Under the HCHV program, the VA provides care and services to homeless or seriously mentally ill veterans, including (1) outreach services; (2) care, treatment, and rehabilitative services; and (3) therapeutic transitional housing assistance. The bill also extends authorization through FY2029 for a program under which the VA establishes sites in larger metropolitan areas to provide comprehensive services to homeless veterans. The bill also provides that under the HCHV program, a veteran means a person who served in the active military, naval, air, or space service and was discharged or released from service, excluding those who received a dishonorable discharge or were discharged or dismissed under a general court-martial.