Improving Low-Energy GEANT4 Simulations of $^7$Be EC Decay in STJ Detectors for the BeEST Experiment

The BeEST Experiment uses Superconducting Tunnel Junctions (STJs) to search for keV-scale sterile neutrinos in the Electron Capture (EC) decay of 7Be. The ultimate sensitivity of this approach is heavily dependent on a precision characterization of the detector response to a wide range of low-energy radiation emitted in the decay. Detailed ultra-low-energy, multi-process particle simulations in GEANT4 are employed to help describe these processes to high accuracy. In this talk, I will present preliminary results and advancements towards accurate meV-scale GEANT4 simulations.