A 62-year-old woman with type 2 diabetes mellitus is brought to the hospital by her family with a 1-week history of progressive confusion, polyuria, and polydipsia. She had been unwell with fever and cough 10 days ago but did not seek medical care. On examination, she is drowsy but arousable, respiratory rate 16/min (normal), blood pressure 95/60 mmHg, heart rate 120/min, and axillary temperature 37.8°C. Skin turgor is poor. Laboratory investigations show: blood glucose 680 mg/dL, arterial pH 7.32, HCO₃⁻ 18 mEq/L, PaCO₂ 42 mmHg, serum sodium 148 mEq/L, serum osmolality 380 mOsm/kg, blood urea nitrogen 84 mg/dL, and serum creatinine 2.1 mg/dL. Urine ketones are negative. What is the most likely diagnosis, and what is the primary pathophysiological mechanism underlying the severe hypernatremia in this patient?