An 8-day-old male neonate presents to the emergency department with his parents due to increasing lethargy and poor feeding over the past 12 hours. His mother reports he has felt warm to touch, although no temperature was recorded at home. He was born at term via spontaneous vaginal delivery, and the mother received no consistent prenatal care. On arrival, his vital signs are: temperature 38.5℃ (axillary), heart rate 170/min, respiratory rate 65/min with occasional grunting, and blood pressure 60/35 mmHg. Physical examination reveals a floppy infant with reduced spontaneous movements, poor suck reflex, and mottled skin. The anterior fontanelle is soft and flat. Capillary refill time is 4 seconds. Based on the clinical presentation and initial findings, what is the most likely diagnosis and the immediate management strategy, including the most appropriate empiric antimicrobial and antiviral regimen, for this patient?