I think I got it: The two parts of the caliper are connected through the centering screw, the tiny bolt that requires a 2,5mm allen key.

1. Pulling the brake lever pulls down the left-side part; The right-side part moves after being pushed by the casing going up.

When releasing the brake lever, the left-side part moves away from the rim because of its spring, which also moves the right-side part thanks to the centering screw pushing down on the right-side part.

2. Loosening the barrel adjuster on the brake lever moves the non-compressing casing against the right-side part, moving that part towards the rim; As a result, thanks to the centering screw and the spring, the left-side part also moves towards the rim.