A 58-year-old man from Bangalore presents with sudden-onset severe right upper quadrant pain, fever (39.2°C), and hypotension (BP 100/62). On examination, he is toxic-looking with severe RUQ tenderness and guarding. Ultrasound shows a large stone (2.5 cm) impacted in the gallbladder neck, marked wall thickening (6 mm), extensive pericholecystic fluid, and free intraperitoneal fluid. WBC is 16,000/μL. Serum bilirubin is 1.2 mg/dL (normal). What is the most likely diagnosis and the most appropriate immediate management?