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Wi-Fi in the enterprise - characterized by overlapping Wi-Fi cells - constitutes the design challenge for next-generation networks. Standardization for recently started IEEE 802.11be (Wi-Fi 7) Working Groups has focused on significant medium access control layer changes that emphasize the role of the access point (AP) in radio resource management (RRM) for coordinating channel access due to the high collision probability with the distributed coordination function (DCF), especially in dense overlapping Wi-Fi networks. This paper proposes a novel multi-AP coordination system architecture aided by a centralized AP controller (APC). Meanwhile, a deep reinforcement learning channel access (DLCA) protocol is developed to replace the binary exponential backoff mechanism in DCF to enhance the network throughput by enabling the coordination of APs. First-Order Model-Agnostic Meta-Learning further enhances the network throughput. Subsequently, we also put forward a new greedy algorithm to maintain proportional fairness (PF) among multiple APs. Via the simulation, the performance of DLCA protocol in dense overlapping Wi-Fi networks is verified to have strong stability and outperform baselines such as Shared Transmission Opportunity (SH-TXOP) and Request-to-Send/Clear-to-Send (RTS/CTS) in terms of the network throughput by 10% and 3% as well as the network utility considering proportional fairness by 28.3% and 13.8%, respectively.