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Arrays of Josephson junctions can be tuned through anomalous metallic, quantum-critical, and insulating regimes. We introduce an alternative experimental probe, capturing microwave radiation across all three regimes, using a two-dimensional array of superconductor-semiconductor hybrid Josephson junctions as a model system. Our approach allows calibration of the sample’s circuit parameters and provides isolation from measurement back-action effects. We measure the radiation temperature of the anomalous metal and find that it is hotter than both the quantum-critical and insulating regimes. We further show that the anomalous metallic regime is more susceptible to additional heating than other regimes, explaining its emergence in otherwise thermalized systems. Turning to the quantum-critical regime, we discover nonlinear scaling of radiative noise with applied bias, consistent with theoretical predictions of universal nonequilibrium behavior at quantum-critical points.