the body won't turn protein to body fat

It can and will if you eat enough excess protein. Amino acids are used for protein synthesis, but there is a limit to protein synthesis and dietary protein that exceeds that can be stored as fat.

The body will not normally urinate out protein, even a tiny amount of protein in urine is pathological. Fecal material contains protein, but mainly from dead gut bacteria and dead intestinal cells. The body normally absorbs dietary amino acids efficiently and failure to do so would be pathological malabsorption.

Amino acids are a form of chemical energy, the body can only synthesize so much protein (obviously) and eventually excess amino acids, if present, will be converted to fat, through gluconeogenesis, amino acid synthesis, and lipogenesis.

it can turn carbs into body fat in a surplus but prefers to use carbs as energy

The human body has very limited capacity to store carbohydrates directly. Beyond that, surplus food energy in the form of carbohydrates will be stored as body fat. It is very easy to get fat on a low fat diet with many carbohydrates.

dietary fat will turn to body fat if you're in a surplus

All excess calories from any source will be turned into body fat if you're in a surplus.