Family Stability and Opportunity Vouchers Act of 2023 This bill establishes a voucher program through which public housing agencies (PHAs) shall offer support services to help families who have children and are unstably housed, live in an area of concentrated poverty, or are at risk of being displaced from an opportunity area for children move to areas with access to high-performing schools or high-quality childcare and early education. The Department of Housing and Urban Development must provide assistance to PHAs on a competitive basis to implement the program.