The static air pressure seen by the aircraft does not change with the aircraft's velocity.
Your confusion is from a common misinterpretation of Bernoulli's principle. It is not true that a fluid's pressure will decrease simply by virtue of flowing faster. After all, this violates the idea that physics should be the same in all inertial frames.
Here is a simple counterexample to the typical interpretation of the Bernoulli principle. Consider a tube of infinite length and uniform diameter with some gas sitting in it. Now consider various coordinate systems with a velocity in the direction of the tube. In these different coordinate systems, the velocity of the gas will be different, but we expect the force on the walls of the tube due to the fluid's pressure to be the same in all cases. (The tube is not going to rupture simply because of a choice of coordinate system!)
Instead, Bernoulli's principle says that, in a given flow (say, along a streamline), a local increase in velocity is associated with local decrease in pressure. The canonical example is fluid flow through a tube with a constriction (a venturi).
Quoting from the Wikipedia article for Bernoulli's principle:
Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. ... If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest.
Note the emphasis on relative changes occurring on a streamline.
The specific flaw in your argument is here:
Now the fluid is accelerated along a streamline, and hence the static pressure should drop according to the relation given above.
In the wind tunnel, something has to do work to accelerate the air to the wind tunnel velocity, adding energy to the flow, which violates the conservation of energy assumption in Bernoulli's principle.