A 28-year-old man is brought to the emergency department 2 hours after a flame burn injury sustained while cooking. On examination, the affected area over his right forearm and hand shows a leathery, charred appearance with a dark brown-black color. The skin is painless to touch, and there is no blanching on pressure. The surrounding area shows blistering and erythema. What is the depth classification of the burn injury on the right forearm?