Energy capture photochemistry with ionizing radiation?
The energy scales of x-ray and gamma radiation are too large to be chemically helpful in the way that the electromagnetic around visible wavelengths is.

X-rays, if absorbed, typically excite core electrons of atoms. As we know, core electrons are (to a first approximation) not affected by the details of chemical bonding in the valence, so any attempt to use a chemical bonding motif to capture x-rays (e.g. conjugation of porphyrins) is of the wrong energy scale. You could use the Auger Effect to eject a valence electron with x-ray scale energy. This does constitute radiationless conversion of the light into electronic energy, but it doesn't meet your qualifications for storing and extracting work.

Gamma rays are typically produced by the decay of one nuclear state to another, and are vastly different in energy scale than electronic states, so there's no way to do chemistry with gamma radiation, at least directly. The Mössbauer effect does allow us to use gamma rays to understand local structure in a crystal, but even then most of the energy is absorbed into exciting the nuclear state, which we cannot control chemically.