We report on measurements of dissipation and frequency noise at millikelvin temperatures of nanomechanical devices covered with aluminum. A clear excess damping is observed after switching the metallic layer from superconducting to the normal state with a magnetic field. Beyond the standard model of internal tunneling systems coupled to the phonon bath, here we consider the relaxation to the conduction electrons together with the nature of the mechanical dispersion laws for stressed/unstressed devices. With these key ingredients, a model describing the relaxation of two-level systems inside the structure due to interactions with electrons and phonons with well separated timescales captures the data. In addition, we measure an excess 1/f-type frequency noise in the normal state, which further emphasizes the impact of conduction electrons.