Inspired by noncommutative geometry in string theory, we introduce extended derivatives in black hole physics by incorporating a real antisymmetric rank-2 tensor, exhibiting similarities with certain string-theoretic fields. Within the gauge-theoretic formulation of gravity based on the de Sitter group, we first derive the corresponding black hole solutions by solving the Einstein field equations. We then investigate their thermodynamic properties, focusing on stability analysis, critical behavior, and phase transitions. In particular, we analyze the P–V criticality of the obtained solutions and compute the Gibbs free energy, which reveals behavior analogous to Van der Waals phase transitions. Furthermore, by combining analytical and numerical results, supported by CUDA-based computational techniques commonly used in machine learning, we establish constraints on the deformation parameter (B) and the charge (Q). Specifically, we identify parameter ranges for which the black hole system exhibits thermodynamic behavior similar to that of a Van der Waals fluid.