A 28-year-old man with known type 1 diabetes mellitus presents to the emergency department with a 2-day history of polyuria, polydipsia, and progressive lethargy. He had missed his insulin injections for 3 days due to financial constraints. On examination, he is drowsy, respiratory rate 28/min with deep laboured breathing, blood pressure 110/70 mmHg, and heart rate 110/min. His breath has a fruity odour. Laboratory investigations reveal: blood glucose 580 mg/dL, arterial pH 7.18, HCO₃⁻ 10 mEq/L, anion gap 18, serum sodium 128 mEq/L, serum potassium 6.2 mEq/L, and serum creatinine 1.8 mg/dL. Urine dipstick shows 4+ ketones and 2+ protein. What is the most appropriate immediate management after securing airway and establishing IV access?