State Veterans Homes Relief Act of 2021 This bill appropriates $500 million to the Department of Veterans Affairs (VA) to fund projects on the grant program priority list for construction of state homes that are approved by the VA prior to the enactment of this bill. A state home is a home established by a state for veterans who are disabled by age, disease, or otherwise and incapable of earning a living because of such disability. The term also includes a home that furnishes nursing home care for veterans.