Airplanes do correct for the Coriolis effect. They constantly make adjustments to counter forces that try to push them away from the planned route, including the Coriolis force.
Flat-Earthers claim the Coriolis effect does not appear to affect airplanes, and they use it to “prove” that Earth is stationary. In reality, the Coriolis effect does affect airplanes, and we do have to correct for it. But the effect is tiny, and we can safely ignore it in flight planning.