Interpretation of subsurface storage characterization heavily depends on the quality and continuity of well log data. However, missing measurements and anomalous responses are common due to geological heterogeneity, tool limitations, and borehole conditions. Conventional machine learning and deep learning methods, such as Long Short-Term Memory (LSTM) and Convolutional Neural Networks (CNNs), have improved data recovery but remain constrained by the need for extensive retraining, labeled data, and basin-specific tuning. In this study, we present a novel application of a pre-trained time-series foundation model, TimeGPT, for well log imputation and anomaly detection that enables zero-shot inference across different basins and lithologies. This work represents one of the first applications of a generative pre-trained transformer GPT-based model to geoscientific time-series data, bridging recent advances in AI foundation modeling with subsurface analytics. We applied and fine-tuned TimeGPT using multi-log datasets (Gamma ray, Deep resistivity, Bulk density, Neutron porosity, and Sonic transit time) from the Groningen gas field in the Netherlands, and validated its performance against conventional machine learning and deep learning benchmarks. The proposed approach achieved a mean absolute error (MAE) between 0.02% and 0.32%, demonstrating a >10% improvement over conventional models and comparable accuracy to advanced architectures such as bidirectional LSTM and Transformers. Moreover, the model attained 93% anomaly detection accuracy using conformal prediction intervals, effectively distinguishing among geological heterogeneity, tool noise, and borehole-related anomalies. The time-series foundation models can generalize well across different geological settings without retraining, enabling basin-agnostic and data-efficient well log analysis. The integration of self-attention mechanisms and conformal uncertainty quantification provides robust, interpretable predictions for real-world reservoir characterization. This work highlights the transformative potential of generative AI in geosciences, advancing well log interpretation toward scalable, low-risk, and foundation-model-driven analytics for the next generation of subsurface intelligence.