if you look for the energy you can't think about the aircraft alone - it's flying throught the air and what happens to the air must also be taken into consideration. You are correct that in level, non-accelerated flight the energy of the airplane doesn't change. As you wrote the work done is the product of force times displacement. And in level, non-accelerated flight both the vertical forces (gravity and lift) as well as the horizontal forces (drag and thrust) cancel exactly (otherwise the airplane would accelerate, i.e. it would start to rise or fall or get slower or faster). And since there's no net force no work is done and the energy of the airplane remains unchanged. This doesn't depend on the reference system, in each reference frame the net force on the airplane is zero.
Things are different for the air you're flying through. The air you hit must be shoved out of the way (and to get it to start moving it must be accelerated). The air going through the engines gets accelerated, thereby generating the thrust that balances the drag. And the air flowing around the wings gets pushed downwards, producing the lift that keeps you up against gravity. Whenever something is made to move energy is needed (if you accelerate something from zero speed to a speed of v the energy required to do so is half its mass times v squared, i.e. the kinetic energy it obtains). And this is where all the chemical energy from the fuel goes to (disregarding losses) - it ends up in accelerating the air you're flying through.
The drag the airplane experiences has two components. First there's the "normal" drag (also sometimes called "profile drag") that also would be there without wings, it's due to the air getting pushed out of the way and friction with the body of the airplane. And then there's the so called "induced drag" which results from the wings pushing air downwards. Normal drag roughly increases with the square of the speed of the airplane while the induced drag drops with speed (always assuming level flight at all speeds and adjusting the AoA to maintain level flight). At low speeds the induced drag is the major contribution to the total drag, at higher speeds it's the "normal" drag. And at one speed there's a "sweet spot" where the total drag has a minimum, and that's the speed for the best L/D ratio.