For a two-particle system, which of the following quantities...

The potential energy of a two-particle system interacting via conservative forces (such as gravitational or electrostatic forces) is a function of their configuration. This means it depends exclusively on the separation distance between the two particles, $U = U(r)$.

Kinetic energy depends on the velocities of the particles.

Total mechanical energy and total energy are the sum of kinetic and potential energies, so they depend on both the separation and the velocities of the particles.

Therefore, only potential energy depends exclusively on the separation.