Dephasing-driven suppression of superradiance and metastable dynamics in the anisotropic open Rabi model

Finite-component light-matter systems realize dissipative phase transitions in a single controllable atom-cavity setup, but how atomic dephasing - ubiquitous in real cavity- and circuit-QED devices - affects this criticality remains unknown. We study the anisotropic open Rabi model under cavity decay, spontaneous emission, and atomic dephasing together. We show that when spontaneous emission stabilizes a long-lived metastable superradiant phase, atomic dephasing actively competes with it - eroding its coherence and shortening the lifetime. This direct competition reveals that a dissipation channel's microscopic character, not its strength, controls its nonequilibrium criticality - a distinction directly tunable via independent spontaneous-emission and dephasing rates in circuit-QED and trapped-ion platforms.