Why does searing meat in a hot pan create a brown, savory crust?

Answer: Proteins and sugars react on the hot surface to form brown pigments.

Proteins and sugars react on the hot surface to form brown pigments. ✓ — On a hot surface, amino groups in the meat react with sugars in the Maillard reaction. This creates brown pigments and aroma compounds. It explains a seared crust, not every color change inside cooked meat.

Bacteria on the surface die and leave behind dark residues. — Wrong. Heat does kill surface bacteria, so cooking does make meat safer, but dead bacteria do not leave enough dark material to color the meat. The brown surface comes from reactions among the meat's own proteins and sugars.

Melted fat turns brown as it caramelizes on the meat. — Wrong. Fat does melt and can make the surface look glossy, and sugars can caramelize, but fat itself does not caramelize into brown pigments. The brown crust mainly comes from protein-sugar reactions.