State of health (SOH) is a key indicator for safety monitoring, lifetime assessment, and maintenance decisions in lithium-ion battery management systems. However, differences in initial capacity, degradation rate, local capacity variation, and health-indicator evolution often cause models trained on limited source cells to produce biased predictions and unstable trajectories on unseen cells. To address this challenge, we develop the Energy-Aware Warm-Up with Degradation-Consistency Constraints (EWDC) framework for unseen-cell SOH prediction. EWDC couples partial-charge health-indicator extraction, health-indicator graph encoding, cycle-to-cycle degradation-increment prediction, and recursive SOH-trajectory reconstruction. Within-dataset leave-one-battery-out validation was conducted separately on the NASA and CALCE-CS2 datasets. Across the eight held-out cells, EWDC achieved average RMSE, MAE, and $R^2$ values of 1.21%, 0.65%, and 0.975, respectively. Relative to the GNN baseline, EWDC reduced average RMSE and MAE by 32.19% and 38.83%, respectively. Additional limited-source-battery experiments and ablation studies suggest that EWDC improves within-dataset unseen-cell prediction accuracy.