A 32-year-old woman from rural Maharashtra presents to the emergency department with a 3-day history of severe vomiting and abdominal pain following acute gastroenteritis. On examination, she is lethargic, with a respiratory rate of 28/min and fruity-smelling breath. Blood glucose is 45 mg/dL, arterial pH is 7.28, HCO₃⁻ is 12 mEq/L, and serum ketones are markedly elevated. Liver function tests are normal. Which enzyme deficiency would most directly explain her inability to maintain blood glucose despite the metabolic stress of starvation and acidosis?