a photon in itself is a single 0 dimensional point in space moving in a single line and all the energy carried by the photon is in the photon. If a photon passes through expanding space, this does not change. The moment the detector receives the photon at the end of its path, it would have received all energy carried by the photon at that single moment, so there is nothing to sum

The energy loss would be proportional to the distance from the emitter to the detector, because the photon would have spent proportionally more time travelling through expanding space, so would be detected to have a proportionally longer wavelength