Battery-constrained Internet of Things (IoT) devices face significant challenges in maintaining long-term uplink data collection, especially in network-limited scenarios. This paper investigates a Ground-Air cooperative Wireless-Powered IoT network (GA-WPIoT), where ground power beacons (GPBs) provide radio-frequency energy supply and unmanned aerial vehicles (UAVs) serve as flexible aerial access points for IoT data collection. Unlike conventional UAV-enabled wireless-powered solutions, GA-WPIoT decouples energy transfer and data collection, reducing the hardware and energy burden of UAVs. To capture the device-level performance variations among IoT devices, we develop a stochastic geometry-based analytical framework, where UAVs are modeled by a Matérn hard-core point process, IoT devices by a Poisson point process, and GPBs by a finite annular binomial point process. The conditional success probabilities of the GPB-device link (for energy transfer) and the device-UAV link (for data collection) are characterized, and device-level reliability distributions are obtained through the Meta-Distribution based analysis. Numerical results under suburban and urban environments reveal the impacts of UAV altitude and annular GPB deployment on reliability distributions, providing useful guidelines for GA-WPIoT.

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