Retrospective battery characterization is difficult because heterogeneous cells exhibit widely varying cycling records due to chemistry, test protocol, format, capacity, and operating conditions. An endpoint charge‑discharge curve captures the local state of a single cycle, while a cell‑level lifecycle terrain (e.g., the $dQ/dV$ curve) summarizes structural evolution across the entire archived trajectory. We introduce STEK, a framework that fuses the cell‑level terrain with an endpoint‑derived structural proxy via a quality‑proxy‑conditioned gate.\ \ At the representation level, bounded FiLM (Feature‑wise Linear Modulation) and a validity‑gated residual head refine the endpoint‑curve embedding while preserving a curve‑based prediction pathway. Battery type and optional material‑text descriptors further condition an identity‑centered low‑rank linear map, providing a Koopman‑inspired cross‑channel consistency objective without explicit temporal dynamics or rollout.\ \ Under the fixed seven‑output MIX‑battery protocol, the full retrospective setting improves aggregate performance over endpoint‑only learned baselines across multiple temporal backbones, reflecting both the added archived context and the modeling design. With matched auxiliary inputs, STEK outperforms direct concatenation and quality‑unaware FiLM; descriptor‑removal ablations show graceful fallback to the endpoint pathway. Deterministic rules remain preferable for directly recoverable capacity summaries. The method targets archive harmonization rather than online estimation from a single cycle.\ \ Review: STEK’s integration of global lifecycle terrain with local endpoint information yields a cross‑channel consistency regularization that markedly boosts performance in retrospective battery multi‑target estimation, while maintaining robustness to missing descriptors.