Is the Reynold's number a function of the fluid flow stream or the obstruction?
Maybe it helps to see the Reynolds number as the ratio of inertial to viscous forces. High flow speeds mean high inertial forces, and so lead to high Reynolds numbers. Viscous effects are strongest when the airflow hits the obstacle, and become less strong the longer the air flows around a body, so a short flow path has a low Reynolds number.

In the end it does not matter if the length of the flow or its speed drive the Reynolds number up. It is the combination of both. I am neglecting the gas properties here, because I assume we talk about air at moderate temperature and do not want to make the issue more complex.

Airfoils have no Reynolds number per se, flow conditions have. The Reynolds number of a measurement can be doubled by making the chord of the airfoil twice as long at the same airspeed, or by doubling the airspeed at the same chord. The wing of an airplane operates in a range of Reynolds numbers, depending on flight speed. That is why polar diagrams normally contain the results of several test runs rsp. computations, each at a different Reynolds number.

Sometimes you see airfoils which are optimized for a particular Reynolds number. To avoid early separation, the recompression area of an airfoil must become proportionally longer the smaller the Reynolds number is at which the airfoil is supposed to function well. At higher Reynolds numbers such an airfoil will still work, but will produce more drag than one which is optimized for a higher Reynolds number. The Reynolds number allows the aircraft designer to pick an airfoil that works well at the combination of speed and chord length for which that airplane is designed.