Constraining Redshift Parametrization Models with Recentmost Data : Impacts on an Accretion Disc around Finslerian Kiselev Black Hole

We investigate the evolution of black hole mass within a cosmological background modeled by a Modified Chaplygin Gas (MCG) under various dark energy equation of state parametrizations, including Linear, Logarithmic, CPL, JBP models. The logarithmic mass ratio $\log_{10}[M(z)/M_0]$ is found to be highly sensitive to the redshift-dependent evolution of $\omega(z)$, with gentle slopes in Linear, Logarithmic and CPL models indicating quasi-static accretion and steep slopes in JBP corresponding to rapid late-time variations highlighting transient suppression or enhancement of accretion due to repulsive dark energy effects. Peaks, minima and amplitude offsets in the mass ratio reflect the dynamic interplay between horizon thermodynamics, the evolving pressure of the MCG and cosmic expansion, illustrating how the black hole mass growth is directly influenced by both the temporal evolution of dark energy and the effective gravitational potential of the surrounding cosmic fluid. Our results demonstrate that black hole accretion acts as a sensitive probe of the time-dependent cosmic pressure landscape and provides physical insights into the coupling between local strong gravity and global accelerated expansion.