Guaranteeing stringent data freshness for low-altitude unmanned aerial vehicles (UAVs) in shared spectrum forces a critical trade-off between two operational costs: the UAV's own energy consumption and the occupation of terrestrial channel resources. The core challenge is to satisfy the aerial data freshness while finding a Pareto-optimal balance between these costs. Leveraging predictive channel models and predictive UAV trajectories, we formulate a bi-objective Pareto optimization problem over a long-term planning horizon to jointly optimize the sampling timing for aerial traffic and the power and spectrum allocation for fair coexistence. However, the problem's non-convex, mixed-integer nature renders classical methods incapable of fully characterizing the complete Pareto frontier. Notably, we show monotonicity properties of the frontier, building on which we transform the bi-objective problem into several single-objective problems. We then propose a new graph-based algorithm and prove that it can find the complete set of Pareto optima with low complexity, linear in the horizon and near-quadratic in the resource block (RB) budget. Numerical comparisons show that our approach meets the stringent timeliness requirement and achieves a six-fold reduction in RB utilization or a 6 dB energy saving compared to benchmarks.