Existing generalized few-shot 3D segmentation (GFS3DS) methods typically prioritize enhancing the training of base-class prototypes while neglecting the rich semantic information within background regions for future novel classes. We introduce a novel GFS3DS learner that strategically leverages background context to improve both base prototype training and few-shot adaptability. Our method employs foundation models to extract semantic features from background points and grounds on text embeddings to cluster background points into pseudo-classes. This approach facilitates clearer base/novel class differentiation and generates pseudo prototypes that effectively mimic novel support samples. Comprehensive experiments on S3DIS and ScanNet datasets demonstrate the state-of-the-art performance of our method in both 1-shot and 5-shot tasks. Our approach significantly advances GFS3DS by unlocking the potential of background context, offering a promising avenue for broader applications. The GitHub repository of our implementation will be released upon publication.