A 58-year-old man with a history of liver cirrhosis presents to the emergency department with confusion, abdominal distension, and fever (38.8°C). He is haemodynamically unstable with MAP 55 mmHg. Diagnostic paracentesis shows turbid fluid with a neutrophil count of 450 cells/mm³ (0.45 × 10⁹/L). What is the diagnosis and most appropriate initial antibiotic?