We investigate a class of effective electrodynamic extensions in which a minimal photon rest mass is treated together with a constitutive sector independent of the mass parameter. Here, "minimal" denotes a parametrically small positive scale compatible with experimental upper bounds, not an experimentally established lower bound on mγ. Starting from the relativistic dispersion relation of a massive vector field, we derive the corresponding group-velocity correction and formulate a constitutive closure for light—matter interaction that distinguishes intrinsic photon mass, medium-induced effective mass, and equivalent interaction energy. We impose energy—momentum conservation, thermodynamic admissibility, stability, recovery of limiting theories, and experimental identifiability. We further construct a conventional electromechanical null model including Maxwell stress, elasticity, electrostriction, photoelasticity, dissipation, and thermal response. The resulting framework shows that a local scalar coupling linear in electromagnetic energy density is not independently identifiable in the isotropic linear regime unless it carries an additional dynamic, tensorial, geometric, or nonlocal signature. We formulate differential observables and a hierarchy of null hypotheses for separating Proca-like effects from conventional medium response, and discuss constraints from quasi-static magnetic fields, dispersive propagation, fast radio bursts, and magnetohydrodynamic environments. The theory is presented as a falsifiable effective framework: compatibility with current bounds is not interpreted as detection, and the photon-mass sector is not used to infer macroscopic return, gravitational capture, or stellar feedback.