Transition-edge sensors (TESs) exploit the resistive transition of a superconductor to detect minute changes in temperature. While significant progress has been made in understanding the temperature- and current-dependent resistive transition in these devices, important aspects of TES behavior under bias remain unresolved. In particular, existing TES models largely neglect spatial variations in the superconducting state and current distribution arising from device geometry and proximity effects associated with the superconducting leads and normal metal features. Using scanning superconducting quantum interference device (SQUID) microscopy (SSM), we directly image local superconducting properties and transport current in two molybdenum-gold (MoAu) X-ray TES designs. We measure the local diamagnetic response to identify superconducting regions in devices voltage-biased within the transition and the Oersted field generated by the transport current to reconstruct the corresponding current distribution. We observe bias-dependent reconfigurations of the current distribution that track current-induced changes in superconducting regions, highlighting the importance of mesoscale spatial variations for TES device physics, operation, and design.