In unmanned aerial vehicle (UAV)-assisted wake-up radio (WuR)-enabled internet of things (IoT) networks, UAVs can instantly activate the main radios (MRs) of the sensor nodes (SNs) with a wake-up call (WuC) for efficient data collection in mission-driven data collection scenarios. However, the spontaneous response of numerous SNs to the UAV's WuC can lead to significant packet loss and collisions, as WuR does not exhibit its superiority for high-traffic loads. To address this challenge, we propose an innovative receiver-initiated WuR UAV-assisted clustering (RI-WuR-UAC) medium access control (MAC) protocol to achieve low latency and high reliability in ultra-low power consumption applications. We model the proposed protocol using the $M/G/1/2$ queuing framework and derive expressions for key performance metrics, i.e., channel busyness probability, probability of successful clustering, average SN energy consumption, and average transmission delay. The RI-WuR-UAC protocol employs three distinct data flow models, tailored to different network traffic conditions, which perform three MAC mechanisms: channel assessment (CCA) clustering for light traffic loads, backoff plus CCA clustering for dense and heavy traffic, and adaptive clustering for variable traffic loads. Simulation results demonstrate that the RI-WuR-UAC protocol significantly outperforms the benchmark sub-carrier modulation clustering protocol. By varying the network load, we capture the trade-offs among the performance metrics, showcasing the superior efficiency and reliability of the RI-WuR-UAC protocol.