A 42-year-old woman with a 10-year history of type 2 diabetes mellitus presents to the emergency department with a 3-day history of polyuria, polydipsia, and progressive dyspnea. She is drowsy but arousable. Vital signs: RR 28/min, BP 110/70 mmHg, HR 110/min. Laboratory findings: pH 7.18, PaCO₂ 22 mmHg, HCO₃⁻ 8 mEq/L, Na⁺ 132 mEq/L, K⁺ 6.2 mEq/L, glucose 580 mg/dL, serum osmolality 320 mOsm/kg. Anion gap 24 mEq/L. Urine ketones: strongly positive. What is the primary acid-base disorder and what is the mechanism of the respiratory response?