The open anisotropic quantum Rabi model (QRM) is studied in this work, with an explicit $A^2$ term incorporated. It is shown that, in the presence of cavity loss, anisotropy allows the steady-state superradiant transition to occur even when the $A^2$ term prohibits the transition in the isotropic case. The $A^2$ term reshapes and enriches the known steady-state phase diagram of the open anisotropic QRM, leading to an asymmetric structure composed of normal, superradiant, and bistable phases. In particular, the nonequilibrium tricritical points are generally separated from the merger point of the two critical branches that bound the superradiant region. Isolated bistable regions also emerge, and the number and positions of tricritical points are reduced. Notably, the anomalous photon-number fluctuation scaling is associated with the merger of the two critical branches, rather than with the tricritical points. These results clarify the role of the $A^2$ term contribution in the steady-state structure of the open anisotropic QRM and provide a refined extension of the previously known dissipative phase diagram, offering a useful theoretical reference for future studies of related open light-matter systems.

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• Dissipative dynamics
• Master equation
• Rabi model