Magnet Schools Accessibility, Growth, and Nonexclusionary Enrollment Transformation Act of 2022 or the MAGNET Act of 2022 This bill reauthorizes through FY2025 and expands the Magnet Schools Assistance Program (MSAP), which provides grants to eligible local educational agencies (LEAs) to establish and operate magnet schools that are operated under a court-ordered or federally approved voluntary desegregation plan. The bill authorizes a new grant program under MSAP to award grants to LEAs and state educational agencies for increasing diversity in magnet schools.