Ground-based astronomical surveys inadvertently capture streaks from satellites and space debris crossing their fields of view. These incidental observations from wide-field instruments such as OmegaCAM on the VST offer valuable opportunities to characterise resident space objects without the need for dedicated observing time. We developed an automated deep-learning pipeline to detect and classify streaks in the OmegaCAM archive, enabling large-scale analyses of space object populations and their impact on astronomical data. The pipeline combines an adapted Hough transform lookup-based convolutional neural network (HT-LCNN) for initial streak detection on raw images with a VGG6-based CNN classifier to reject false positives. We augmented a manually annotated dataset of 384,000 patches from archive images with physically simulated streaks. Following a detection, we applied astrometric calibration and cross-matched the results with the space-track catalogue. We find the detector achieves F1-scores of 0.966 (validation) and 0.958 (test) on the augmented dataset, detecting $>95%$ of artificial streaks with a signal-to-noise ratio of text S/N >4. On real 2023 data, the precision drops to 0.783 due to image variability, but the classifier boosts it to 0.990, while retaining 97% of true positives and rejecting $>96%$ of false positives. Applied to one year of VST observations (1,246,048 OmegaCAM CCD frames), the pipeline identified 25,335 streaks, including more than 20% uncorrelated with catalogue entries; finally, 16.9% of images revealed some level of contamination. The pipeline demonstrates robust performance on real archival data and successfully uncovers faint uncatalogued objects, highlighting the potential of survey archives for debris monitoring.