A 62-year-old man with type 2 diabetes mellitus presents with a 5-day history of progressive confusion, polyuria, and weakness. On examination, he is drowsy but arousable, with dry mucous membranes and skin turgor loss. Capillary blood glucose is 580 mg/dL. Arterial blood gas shows pH 7.32 with HCO₃⁻ 16 mEq/L. Serum osmolality is 335 mOsm/kg. Which investigation would be most helpful in distinguishing HHS from DKA in this clinical scenario?