Foreign Animal Disease Prevention, Surveillance, and Rapid Response Act of 2023 This bill provides additional funding for Animal and Plant Health Inspection Service (APHIS) animal disease prevention and management programs and reauthorizes the programs through FY2028. Specifically, the bill reauthorizes and provides additional funding for the National Animal Health Laboratory Network (a nationally coordinated network and partnership of federal, state, and university-associated animal health laboratories that provides animal health diagnostic testing to detect biological threats to the nation's food animals); the National Animal Disease Preparedness and Response Program (which allows APHIS to partner with states, tribes, producer organizations, universities, and others to carry out projects that enhance local, regional, and national capabilities to prevent, prepare for, and respond to animal disease outbreaks); and the National Animal Vaccine and Veterinary Countermeasures Bank (which allows the Department of Agriculture to stockpile animal vaccines and related products to use in the event of an outbreak of foot-and-mouth disease or other high-impact foreign animal diseases).