  We demonstrate an Al superconducting quantum interference device in which the
Josephson junctions are implemented through gate-controlled proximitized Cu
mesoscopic weak-links. The latter behave analogously to genuine superconducting
metals in terms of the response to electrostatic gating, and provide a good
performance in terms of current-modulation visibility. We show that, through
the application of a static gate voltage, we are able to modify the
interferometer current-flux relation in a fashion which seems compatible with
the introduction of $\pi$-channels within the gated weak-link. Our results
suggest that the microscopic mechanism at the origin of the suppression of the
switching current in the interferometer is apparently phase coherent, resulting
in an overall damping of the superconducting phase rigidity. We finally tackle
the performance of the interferometer in terms of responsivity to magnetic flux
variations in the dissipative regime, and discuss the practical relevance of
gated proximity-based all-metallic SQUIDs for magnetometry at the nanoscale.
