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Effective multi-task learning for surgical scene understanding is fundamentally hindered by annotation granularity mismatch; temporal workflow tasks such as phase recognition, step recognition and anticipation benefit from dense frame-level supervision, whereas pixel-level spatial tasks including instrument segmentation and action recognition are only sparsely annotated on selected keyframes due to prohibitive labeling costs. This supervision imbalance undermines shared representation learning and limits joint optimization across heterogeneous surgical tasks. To address this, we propose Flow-guided Annotation for Robust Operating Scenes (FAROS), a flow-guided label interpolation framework, that combines zero-shot segmentation-based mask propagation with optical flow estimation to overcome the limitations of appearance-based propagation under challenging surgical conditions such as occlusion, smoke, and motion blur, generating temporally consistent dense pseudo labels from sparse keyframe annotations. The densified instrument masks and action labels are integrated into a unified Transformer-based multi-task framework that jointly learns surgical phase recognition, step recognition, anticipation, instrument segmentation, and action recognition, enabling balanced optimization between dense temporal supervision and sparse spatial supervision. The label interpolation quality of FAROS is first validated on the DAVIS 2017 benchmark under a sparse ground-truth protocol, confirming robust propagation beyond the surgical domain. Extensive experiments on GraSP, MISAW, and AutoLaparo benchmarks further demonstrate that FAROS significantly improves cross-task representation learning and enhances holistic surgical scene understanding performance across spatio-temporal tasks.