A 3-year-old boy from rural Maharashtra is brought to the paediatric emergency department with a 2-day history of progressive lethargy, vomiting, and ataxia. His mother reports he became irritable after a high-protein meal yesterday. On examination, he is drowsy, with a temperature of 37.2°C, heart rate 110/min, and respiratory rate 28/min. There is mild hepatomegaly. Serum ammonia is 380 μmol/L (normal <50), arterial pH 7.32, HCO₃⁻ 16 mEq/L. Plasma amino acid profile shows elevated glutamine and alanine. Urine orotic acid is markedly elevated. Which enzyme deficiency is most likely responsible for this presentation?