How do we know that bending of light around stars is due to bending of space-time and not diffraction?

  1. We know this because the position of the apparent star is perfectly matching the GR calculations about bent spacetime, depending on a few things including the mass of the star (the one in between that bends spacetime, in your case the Sun).

  2. What you are describing, interference, would not depend on the same way on the mass, the density, stress-energy and a few more things as GR describes bent spacetime.

  3. There were numerous calculations and experiments like the Shapiro test and they all perfectly gave the matching numbers according to GR.

  4. Interference would not depend on the same things, for example interference would react differently on the size/mass ratio or density of the star, whereas in GR it really matters what your star's energy density, for example, is compared to its size, for example, a black hole in your case would have an interference of what? I believe that interference would not even work with a black hole.

On one hand, a typical diffraction angle $\theta$ for light with wavelength $\lambda$ by a spherical obstacle with the radius $R$ of the Sun is $$\theta~\sim~\frac{\lambda}{R}~\sim~~\frac{10^{-6} \text{ m} }{10^{9} \text{ m}}~\sim~10^{-15}\text{ rad};$$ while on the other hand, the gravitational bending/deflection of light by the Sun $$\theta~=~\frac{2r_s}{R}~\approx~\frac{2\cdot 3 \text{ km} }{7 \cdot 10^5\text{ km}}~\sim~10^{-5}\text{ rad}$$ is a roughly 10 orders of magnitude bigger!