A 6-year-old girl presents to the orthopedic clinic 3 days after sustaining a supracondylar fracture of the humerus (Gartland type II) managed with closed reduction and posterior slab immobilization in the emergency department. On examination, she has weakness of wrist and finger extension but normal sensation in the first web space. Grip strength is 2/5 on the affected side. What is the most likely nerve injury, and what is the recommended management?