The limited inertial support and frequency regulation capability of present power networks have become key technical issues that require further improvement. This paper investigates state-of-charge assessment and coordinated regulation for energy-storage converters operating in grid-forming mode. During actual operation, different battery units may show unequal charge levels, and this imbalance can reduce the stabilizing contribution of the whole storage device. To describe the dynamic characteristics of the battery, a two-order resistor-capacitor equivalent model is constructed. The related model coefficients are obtained through recursive least-square estimation with a forgetting mechanism. Based on the identified model, an EKF estimator is developed to predict the charge state of the battery pack. In addition, according to the PCS dynamic equations and regulation features, a coordinated control method is established for the front-end three-phase PWM converter. Its parameters are further tuned by the DDPG-based reinforcement learning algorithm. The experimental results indicate that the proposed EKF estimation approach can reduce SOC prediction deviations. Tests on the IEEE 39-node New England system also confirm that the designed control method is practical and effective. Overall, the combination of battery charge-state estimation and PCS regulation enhances the operational stability of the grid-supporting storage converter system.