Managing heat generation in lithium-ion batteries during high-rate operation remains challenging due to excessive temperature rise and thermal non-uniformity which can significantly affect the system performance, safety and durability. Although hybrid battery thermal management systems combining the phase change materials coupled with liquid cooling through cold plate have been extensively studied, the use of step-graded phase change material (SG-PCM) within hybrid cooling configurations has not yet been explored for high-rate lithium-ion battery applications. To address this gap, this study numerically investigates a hybrid battery thermal management system integrating liquid cooling with SG-PCM for pouch cell module. The proposed configuration employs a cold plate grooved with twisted serpentine channel through which ternary hybrid nanofluid circulates to enhance convective heat removal. A finite element method based numerical approach is implemented using COMSOL Multiphysics to discretize the governing conservation equations. The coupled system is solved using the PARDISO direct solver with a relative tolerance of 0.001. One-dimensional electrochemical framework is used to predict the volumetric heat generation and imposed as a source term within the three-dimensional thermal model to resolve transient temperature distributions. The Non-Isothermal Flow formulation is adopted to integrate laminar flow and heat transfer within the cooling channels and surrounding solid domains. Effective electro-thermal coupling is ensured by the volume-averaged temperature obtained from the three-dimensional thermal model which is iteratively fed back into the electrochemical model where it influences temperature dependent parameters such as electrode and electrolyte diffusion coefficients, ionic conductivity and state of charge. The results indicate that SG-PCM sustains latent heat absorption compared with uniform PCM which leads to lower peak temperature and improved temperature uniformity. Increasing channel twisting enhances secondary flow structures and increases the wetted surface area which improves the convective heat transfer while higher coolant mass flow rates further suppress temperature rise. The results show that, the proposed hybrid system lowers the module maximum temperature approximately by 9 K and limits temperature non-uniformity to below 4 K relative to PCM only cooling which demonstrate its potential for advanced battery thermal management.