<p>Achieving high-precision joint estimation of the state of charge (SOC) and state of health (SOH) for lithium-ion batteries across diverse operating scenarios remains a critical challenge. To address this issue, this paper proposes a novel mechanism-embedded dual-time-scale joint estimation framework. This framework constructs a unified 5-dimensional (5D) state-space model that physically integrates open-circuit voltage bias compensation with a hysteresis voltage term. Through a dual-time-scale observation architecture and a closed-loop correction mechanism, the framework enables accurate synergistic estimation of states and parameters. To fully verify the generalizability and practicality of the proposed method, comprehensive experiments are conducted based on public datasets from the NASA Prognostics Center of Excellence (PCoE) and Oxford University, covering two distinct battery chemistries (LCO and NMC) under static aging and dynamic driving profiles. Experimental results demonstrate that the proposed framework achieves SOC estimation RMSEs of 0.44% and 0.67% on the NASA and Oxford datasets, respectively, and consistently tracks the SOH evolution trajectory over the full lifecycle, demonstrating favorable global estimation precision and enhanced local tracking stability when compared with representative advanced data-driven methods. Systematic ablation studies further indicate that the dimensional augmentation mechanism and the adaptive error compensation operator contribute substantially to estimation robustness. Moreover, the capacity-triggered mechanism effectively avoids redundant parameter updates, while the closed-loop design prevents pseudo-noise accumulation. Furthermore, the proposed framework demands modest computational resources, requiring an average of 1.52&#xa0;s per execution cycle. These results confirm the computational efficiency and high estimation accuracy of the proposed framework in tracking battery states.</p>