Dirac particles tunnelling, barrow thermodynamics, and gravitational lensing in noncommutative-Finsler spacetimes

Abstract We examine a static and spherically symmetric noncommutative—Finsler black hole geometry in the presence of electromagnetic charge and a surrounding Kiselev fluid. The semiclassical tunnelling of Dirac particles is studied through the Hamilton-Jacobi method in an effectively reduced (2+1)-dimensional sector, yielding the standard Hawking temperature. By introducing a generalized uncertainty principle into the Dirac framework, we derive the GUP-corrected temperature and show that the deformation parameter produces measurable deviations near the horizon. In the thermodynamic sector, we employ the exponentially corrected Barrow entropy and analyse its impact on internal energy, Helmholtz free energy, pressure, heat capacity, and the Joule-Thomson coefficient. The deformation parameter shifts the stability regions and modifies the phase-transition structure. Furthermore, light deflection is investigated using the Gauss-Bonnet method in both vacuum and plasma backgrounds. Homogeneous and radially varying plasma profiles are considered, demonstrating significant changes in the photon sphere radius and critical impact parameter. The results indicate that noncommutative effects, when combined with Barrow-type entropy and plasma influence, leave identifiable thermodynamic and optical signatures, suggesting possible observational relevance in strong gravity regimes.