To address spectrum scarcity and support diverse services, including communication and learning tasks, this paper proposes a novel framework that enables the coexistence of over- the-air federated learning (OTA-FL) users with communication users within a reconfigurable intelligent surface (RIS)-aided cognitive radio network (CRN). The system leverages RIS tech- nology to dynamically adjust the channel environment, thereby mitigating interference among heterogeneous data streams. We derive a closed-form expression to quantify the optimality gap between the actual federated learning (FL) model and the theoretical optimal FL model under varying interference levels in uplink communications. To standardize performance metrics across different user types, we define the achievable computation rate for model aggregation in each OTA-FL training round. The study formulates a hybrid rate maximization problem, involving the joint optimization of transmit power for primary user equipment, multiple secondary user equipment, RIS phase shifts, and the denoising factor at the secondary access point. This complex non-convex problem is reformulated as a Markov deci- sion process and solved using deep reinforcement learning (DRL) approaches, specifically the multi-agent deep deterministic policy gradient (MADDPG). Numerical results validate the MADDPG, demonstrating the effectiveness of the DRL-enhanced RIS-aided hybrid CRN in supporting concurrent uplink transmissions

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