To achieve higher throughput in next-generation Wi-Fi systems, a station (STA) needs to efficiently compress channel state information (CSI) and feed it back to an access point (AP). In this paper, we propose a novel deep learning (DL)-based CSI feedback framework tailored for next-generation Wi-Fi systems. Our framework incorporates a pair of encoder and decoder neural networks to compress and reconstruct the angle parameters of the CSI. To enable an efficient finite-bit representation of the encoder output, we introduce a trainable vector quantization module, which is integrated after the encoder network and jointly trained with both the encoder and decoder networks in an end-to-end manner. Additionally, we further enhance our framework by leveraging the temporal correlation of the angle parameters. Specifically, we propose an angle-difference feedback strategy which transmits the difference between the current and previous angle parameters when the difference is sufficiently small. This strategy accounts for the periodicity of the angle parameters through proper preprocessing and mitigates error propagation effects using novel feedback methods. We also introduce a DL-based CSI refinement module for the AP, which improves the reconstruction accuracy of the angle parameters by simultaneously utilizing both the previous and current feedback information. Simulation results demonstrate that our framework outperforms the standard method employed in current Wi-Fi systems. Our results also demonstrate significant performance gains achieved by the angle-difference feedback strategy and the CSI refinement module.