The displacement is accounted for by the wing theory as tip vortexes; the math works nicely that way.
Yes, ever noticed how most of the water you are pushing backwards with the oars of your dinghy ends up going around in little whirlpools? After the energy has been expended to start it moving backwards, the fact that it starts going around in circles isn't very significant.
The mass and acceleration of previously still water moved backwards equals the work to keep the dinghy working against its skin friction, wave making, and air resistance. The pressure differential on the two sides of the oar blades exactly balances out with the resistance although it's more complicated because of the intermittent application due to return strokes.
Tip vortexes are more complicated because they are also composed of "leakage" of the pressure differential around the end of the foil. They can also be seen as the overall circulation "turning the corner" at the end of the foil. Foil and oar vortexes complicate the simplification of air or water being moved in a direction opposite that of motion or acceleration of gravity but it takes a lot of work to create these vortexes and that's an essential part of the energy balance.
Oar vortexes drift slowly backwards relative to the water. Wing tip vortexes on aircraft gradually drift downwards due to the overall downwards air impulse. I know very well that they drift downwards because I used to fly a small plane in and out of a commercial airport and knowing how to predict the fall and drift of the vortexes was essential to staying alive and much discussed by my flight instructors. I hit a well decayed one unexpectedly passing an airport. It was like running over a 4 x 4 on the highway and the plane was well above our altitude.
