Electronic battery management systems (BMS) require high-precision state-of-charge (SOC) estimation to ensure the reliability of integrated electronic applications. However, the flat voltage plateau of LiFePO₄ batteries poses a significant challenge for electronic sensing and state observation. This paper proposes a synergistic dual-adaptive framework designed for real-time electronic monitoring. The framework integrates a thermodynamic-gradient gain-re-allocation (TG-GRA) mechanism into the recursive least squares algorithm to enhance parameter identification fidelity. Furthermore, a current-adaptive augmented extended Kalman filter (CAEKF) is developed to optimize the electronic control loop by dynamically adjusting noise covariance and compensating for voltage hysteresis. Experimental validation across 32 dynamic cycles demonstrates that the proposed electronic sensing strategy reduces the root-mean-square error (RMSE) to 1.3%. With its low computational overhead, this framework provides a robust and efficient system-level solution for embedded electronic research and applications.