Firefighter Staffing and Support Act This bill provides additional funding for firefighter staffing and safety grants. Specifically, the bill increases funding levels for FY2023 and sets a formula for funding for FY2024-FY2028 under the Assistance to Firefighters Grants and Staffing for Adequate Fire and Emergency Response grants programs, including for technical assistance. The Federal Emergency Management Agency (FEMA) and the U.S. Fire Administration must submit to Congress and make publicly available reports on (1) plans to improve the grant application process to ease access to such grant funds; and (2) the challenges specific to rural and volunteer fire departments, including an action plan to address such challenges. The bill also provides protections for volunteer firefighters. An employer may not terminate, demote, or discriminate against a volunteer firefighter for providing emergency services as part of a response to an emergency or major disaster.