Accurate channel state information (CSI) is critical for realizing the full potential of multiple-antenna wireless communication systems. While deep learning (DL)-based CSI feedback methods have shown promise in reducing feedback overhead, their generalization capability across varying propagation environments remains limited due to their data-driven nature. Existing solutions based on online training improve adaptability but impose significant overhead in terms of data collection and computational resources. In this work, we propose AdapCsiNet, an environment-adaptive DL-based CSI feedback framework that eliminates the need for online training. By integrating environmental information -- represented as a scene graph -- into a hypernetwork-guided CSI reconstruction process, AdapCsiNet dynamically adapts to diverse channel conditions. A two-step training strategy is introduced to ensure baseline reconstruction performance and effective environment-aware adaptation. Simulation results demonstrate that AdapCsiNet achieves up to 46.4% improvement in CSI reconstruction accuracy and matches the performance of online learning methods without incurring additional runtime overhead.