Energy storage batteries operating under high levels of renewable energy integration face significant power fluctuations and frequent charge-discharge cycles, leading to substantial errors and uncertainties in state-of-charge (SOC) estimation at short time scales. To address this challenge, this paper proposes a novel SOC estimation method by integrating adaptive forgetting factor recursive least squares (AFF-RLS) with a data-driven hybrid architecture based on bidirectional long short-term memory (BiLSTM) and Transformer model. A second-order equivalent RC circuit model is constructed, and AFF-RLS is employed for real-time identification of model parameters, which are subsequently used as input features for the BiLSTM-Transformer model. The learning rate is dynamically adjusted based on error variation, and network parameters are optimized using the Adam algorithm. The method is validated using experimental data obtained from lead-carbon batteries, with its reliability and robustness verified through widely accepted performance metrics, including mean absolute error, mean absolute percentage error, root mean square error, and the coefficient of determination. Comparative experiments against convolutional neural network, Transformer, and LSTM-based models indicate that the proposed SOC estimation method consistently achieves lower estimation errors within 1.5% across varying state-of-health, demonstrating superior accuracy and robustness.