A 28-year-old male presents to the emergency department 6 hours after a stab wound to the posterior aspect of the upper arm at the junction of the middle and distal thirds. On examination, he has intact wrist extension but complete loss of finger extension at the metacarpophalangeal (MCP) joints, inability to extend the thumb at the interphalangeal joint, and loss of sensation over the dorsal first web space. Motor power in the forearm is otherwise intact. What is the most likely nerve injured and at what anatomical level?