This paper studies a priority-aware aerial backhaul segment for emergency communications in a non-terrestrial network (NTN)-enabled 5G/6G setting, where aggregated multiclass traffic is forwarded from a half-duplex decode-and-forward unmanned aerial vehicle (UAV) relay to a gateway through a high-altitude platform (HAP). The considered architecture is motivated by resilient temporary backhaul deployment when terrestrial infrastructure is damaged, overloaded, or unavailable. To capture non-interruptible packet transmissions, strict non-preemptive priorities are imposed at both the UAV and HAP buffers. The UAV→HAP and HAP→gateway (GW) stages are modeled as tandem non-preemptive priority single-server queue with Poisson arrivals and general service times (M/G/1) queues. Wireless service times are induced by Shannon rates under distance-dependent pathloss and Nakagami-m fading, while the HAP→GW hop additionally follows a probabilistic line-of-sight (LoS)/non-line-of-sight (NLoS) mixture. Using the first two service-time moments, we derive tractable per-class mean waiting and sojourn times and obtain an approximate end-to-end delay expression through queue decomposition. The required inverse-logarithmic expectations are efficiently evaluated by Gauss-Laguerre quadrature. Numerical results reveal class-dependent delay, stability, and resource-allocation trade-offs relevant to resilient UAV-HAP backhaul design in future 5G/6G systems.