Accurate carbon price forecasting is essential for emission trading risk management and low-carbon investment decisions. In existing decomposition-prediction frameworks, secondary decomposition targets are typically selected based on statistical complexity rather than domain-informed causality, and standard Long Short-Term Memory (LSTM)-Transformer architectures discard the cell state that encodes long-term temporal memory. These limitations are particularly pronounced where energy-driven causal structures and regime-switching volatility coexist. This study proposes Causal State-driven Network (CaStNet), an intelligent forecasting framework with two core innovations. A Policy-Causality-guided Residual Secondary Decomposition (PCRSD) module replaces entropy-based criteria with Granger causality to select intrinsic mode functions (IMFs) exhibiting significant energy-carbon causal linkages for targeted variational mode decomposition (VMD). A Cell-State-Driven Dual-function Attention (CSDA) mechanism repurposes the LSTM cell state for simultaneously injecting long-term memory into the Transformer and employing the cell-state differential velocity as a volatility proxy to adaptively regulate Top-k attention sparsity. The Artificial Lemming Algorithm (ALA) globally co-optimizes decomposition dimensions and attention boundaries. A Shapley Additive exPlanations (SHAP)–Local Interpretable Model-agnostic Explanations (LIME) interpretability analysis reveals horizon-dependent driver transitions from short-term autoregressive momentum to long-term energy fundamentals, uncovering threshold nonlinearities in energy-carbon transmission channels. Validation on the Shanghai market (2013–2025) achieves point-forecast RMSE = 0.8326 and R² = 0.9777, outperforming all twelve benchmark models. Cross-market testing on the Hubei market yields R² = 0.9487, and expanding-window five-fold cross-validation on the Shanghai dataset yields mean R² = 0.9704, jointly confirming generalization robustness.