Multivariate time-series anomaly detection aims to identify abnormal temporal patterns in complex real-world systems. However, robust unsupervised time-series anomaly detection remains challenging because anomalies can manifest over different temporal ranges and emerge from interactions among variables, while distribution shifts can cause normal patterns to drift over time. To address these challenges, we propose Codebook-based Online-adaptive Multi-scale Embedding for Time-series anomaly detection (COMET), a unified framework with three tightly coupled components. First, Multi-scale Patch Encoder learns correlation-aware patch embeddings by combining variable-specific temporal dynamics with shared inter-variable structure across multiple patch scales. Second, Vector-Quantized Coreset quantizes these embeddings into representative normal prototypes, which are used to detect anomalies through a dual score combining quantization error and density-aware memory distance. Third, Online Codebook Adaptation leverages the same codebook structure to identify reliable normal samples from training-activated codebook entries, and then updates the prototypes through contrastive learning at inference time. Experiments on five benchmark datasets demonstrate that COMET achieves the best performance on 39 out of 45 evaluation metrics compared to seven baselines, showing robust performance across diverse evaluation protocols.

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