The global pursuit of carbon neutrality requires the reduction of carbon emissions in logistics and distribution. The integration of electric vehicles (EVs) and drones in a collaborative delivery model revolutionizes last-mile delivery by significantly reducing operating costs and enhancing delivery efficiency while supporting environmental objectives. This paper presents a cost-minimization model that addresses transportation, energy, and carbon trade costs within a cap-and-trade framework. We develop a multi-depot mixed fleet, including electric and fuel vehicles, and a drone collaborative delivery routing optimization model. This model incorporates key factors such as nonlinear EV charging times, time-dependent travel conditions, and energy consumption. We propose an adaptive large neighborhood search algorithm integrating spatiotemporal distance (ALNS-STD) to solve this complex model. This algorithm introduces five domain-specific operators and an adaptive adjustment mechanism to improve solution quality and efficiency. Our computational experiments demonstrate the effectiveness of the ALNS-STD, showing its ability to optimize routes by accounting for both spatial and temporal factors. Furthermore, we analyze the influence of charging station distribution and carbon trading mechanisms on overall delivery costs and route planning, underscoring the global significance of our findings.