Optical signatures and thermodynamics of Konoplya–Zhidenko black hole surrounded by perfect fluid dark matter

We investigate weak gravitational lensing and shadow properties of the Konoplya–Zhidenko black hole (BH) surrounded by perfect fluid dark matter (PFDM) and a plasma medium. Considering both homogeneous and non-homogeneous (singular isothermal sphere) plasma distributions, we analyze how the dark matter, the deformation parameter, and plasma frequency modify the deflection angle of light rays and BH’s shadow radius. Our results show that plasma enhances light bending and reduces the shadow size, with the largest shadow in vacuum, followed by non-homogeneous plasma, and the smallest in homogeneous plasma. Comparison with Event Horizon Telescope observations of Sgr A* constrains the allowed parameter space, linking theoretical predictions to measured shadow radii. Additionally, we study Hawking temperature, specific heat, and Gibbs free energy, revealing the roles of PFDM and spacetime deformation in BH stability and phase behavior. This analysis provides insights into the observational signatures and thermodynamic properties of deformed BHs embedded in realistic galactic environments.