The rapid integration of renewable energy resources and battery energy storage systems in modern microgrids has increased the need for intelligent energy management frameworks capable of maintaining storage stability, reducing load variability, and enabling real-time operational decisions. Existing approaches generally focus on forecasting, optimization, or reinforcement learning individually and often struggle with renewable intermittency, real-time synchronization, multi-agent coordination, and uncertainty management within a unified framework. To address these limitations, this research proposes the Twin-Driven Multi-Agent Storage Optimization Network (TMASON) for balancing storage load variability through real-time energy optimization. The framework combines LSTM, CNN, and XGBoost for forecasting load demand, renewable generation, and battery state-of-charge, while a Digital Twin integrated with an Extended Kalman Filter provides accurate real-time state estimation. Multi-Agent Deep Reinforcement Learning and Deep Q-Network determine optimal charging and discharging actions, whereas Model Predictive Control and Genetic Algorithm refine energy dispatch under operational constraints. A Neuro-Fuzzy inference system manages renewable uncertainty and load fluctuations. Experimental evaluation demonstrates that TMASON achieves 99.31% accuracy and a storage load balance factor of 0.98, significantly improving prediction accuracy, storage utilization, decision-making efficiency, and overall system stability for next-generation renewable-integrated microgrids.