Where does the energy of a red shifted photon go?

The energy of a cosmological photon does not go anywhere.

Kinetic energy is not an intrinsic property of an object. Its value depends on the observer.

A projectile does indeed have great velocity and consequently kinetic energy, but only if we are stationary in relation to it. If I could move alongside it with its same speed, I could reach out and grab it because from my point of view it is as if it were stationary.

The same is true for photons whose frequency and therefore energy tends to decrease.

When we measure their frequency, we are in a different and incompatible system of reference, moving relative to it with relativistic velocities, as well as being immersed in a different gravitational field.

In short, the travelling photon has not interacted with anything and has neither gained nor lost energy. The difference in energy arises because the observer’s reference system is not the same as that of the reference system that emitted the photon, mainly due to the expansion of the universe.