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Materials of which the refractive indices can be thermally tuned or switched, such as in chalcogenide phase-change alloys, offer a promising path towards the development of active optical metasurfaces for the control of the amplitude, phase, and polarization of light. However, for phase-change metasurfaces to be able to provide viable technology for active light control, in situ electrical switching via resistive heaters integral to or embedded in the metasurface itself is highly desirable. In this context, good electrical conductors (metals) with high melting points (i.e., significantly above the melting point of commonly used phase-change alloys) are required. In addition, such metals should ideally have low plasmonic losses, so as to not degrade metasurface optical performance. This essentially limits the choice to a few noble metals, namely, gold and silver, but these tend to diffuse quite readily into phase-change materials (particularly the archetypal Ge2Sb2Te5 alloy used here), and into dielectric resonators such as Si or Ge. In this work, we introduce a novel hybrid dielectric/plasmonic metasurface architecture, where we incorporated a thin Ge2Sb2Te5 layer into the body of a cubic silicon nanoresonator lying on metallic planes that simultaneously acted as high-efficiency reflectors and resistive heaters. Through systematic studies based on changing the configuration of the bottom metal plane between high-melting-point diffusive and low-melting-point nondiffusive metals (Au and Al, respectively), we explicitly show how thermally activated diffusion can catastrophically and irreversibly degrade the optical performance of chalcogenide phase-change metasurface devices, and how such degradation can be successfully overcome at the design stage via the incorporation of ultrathin Si3N4 barrier layers between the gold plane and the hybrid Si/Ge2Sb2Te5 resonators. Our work clarifies the importance of diffusion of noble metals in thermally tunable metasurfaces and how to overcome it, thus helping phase-change-based metasurface technology move a step closer towards the realization of real-world applications.