Drones, like most airborne aerial vehicles, face inherent disadvantages in achieving agile flight due to their limited thrust capabilities. These physical constraints cannot be fully addressed through advancements in control algorithms alone. Drawing inspiration from the winged flying squirrel, this paper proposes a highly maneuverable drone equipped with agility-enhancing foldable wings. By leveraging collaborative control between the conventional propeller system and the foldable wings-coordinated through the Thrust-Wing Coordination Control (TWCC) framework-the controllable acceleration set is expanded, enabling the generation of abrupt vertical forces that are unachievable with traditional wingless drones. The complex aerodynamics of the foldable wings are modeled using a physics-assisted recurrent neural network (paRNN), which calibrates the angle of attack (AOA) to align with the real aerodynamic behavior of the wings. The additional air resistance generated by appropriately deploying these wings significantly improves the tracking performance of the proposed "flying squirrel" drone. The model is trained on real flight data and incorporates flat-plate aerodynamic principles. Experimental results demonstrate that the proposed flying squirrel drone achieves a 13.1% improvement in tracking performance, as measured by root mean square error (RMSE), compared to a conventional wingless drone. A demonstration video is available on YouTube: https://youtu.be/O8nrip18azY.