Short-video platforms now expose clickable search entries beneath the video player, enabling users to easily express content-induced search intent. However, conventional query recommendation systems on short-video platforms suffer from latency constraints and objective misalignment, while recent generative approaches struggle with noisy content-side metadata and preference drift. To address these issues, we propose OneBar, an end-to-end generative framework for real-time query recommendation for E-Commerce video feeds. OneBar features three key innovations: (1) a collaborative-multimodal intent grounding module that fuses multimodal video understanding and behavior-derived collaborative anchors; (2) a Unified End-to-End architecture equipped with a prompt-compression mechanism for efficient online serving; and (3) a progressive preference learning strategy for efficient preference-internalization, which internalizes hierarchical behavior preferences into the generative policy, eliminating the need for a separately trained reward model. Compared with online base, OneBar increases Query Exposure by 16.91\% and Query Click by 18.68\%, while maintaining a slight Query CTR gain of 0.19\%. The additional search traffic further contributes to 20.36\% more guided orders and 21.67\% higher GMV.