Energy storage systems (ESSs) are critical to the stability, reliability, and flexibility of microgrids (MGs). Dependence on a single ESS constrains operational longevity due to continuous cycling and difficulties in regulating swift load fluctuations. To address this, hybrid energy storage systems (HESSs) integrate various storage technologies, which are crucial for enhancing stability, efficiency, and operational performance of the system. Nonetheless, advanced power management strategies are essential for achieving optimal operation of HESSs due to their intricate characteristics. This study introduces a hybrid energy storage power management system (HESPMS) that integrates a HESS with an adaptive load management system designed for a grid-isolated solar-powered direct current (DC) MG. The adaptive load management component of the system actively equilibrates demand on the consumption side, efficiently controlling alternating current (AC) loads, such as residential loads, in addition to managing electric vehicle (EV) charging loads. The proposed HESPMS allows the SC to manage transients and the battery to supply continuous power, with one source compensating for the other when required, while adaptively aligning load demands with available solar and storage resources to enhance the performance and prolong the lifespan of HESS. Leveraging a fuzzy logic-based maximum power point tracking (MPPT) controller maximizes solar power conversion and generation efficiency. MATLAB/Simulink simulations validate the proposed system's robustness across multiple operational scenarios, demonstrating precise voltage regulation (+/- 0.046), rapid settling time (20 ms), and peak overshoot of 2.53 %. These results underscore the system's resilience and ability to maintain stable operation under dynamic renewable energy conditions.