I don't believe that Bessel beam is a workaround for the diffraction limit in the far-field. That diffraction limit is a universal law for any optical system with a finite-size aperture (i.e. the size of the focusing mirror array). To the extent you're approximating a Bessel beam in the real, physical world, we're still stuck with finite apertures, so it's the same law.
I agree. It would depend on the definition of "far-field" in this example, even for a quasi-Bessel beam there is a near region that maybe useful for this example given a large enough aperture.
This paper [1] demonstrates the reduced power loss of a Bessel beam compared to a Gaussian for various target distances. For targeting GEO, a Bessel beam can be 75% the size of a Gaussian for the same halving of power-loss.
In reality, I think a Gaussian beam is fine - and much simpler to engineer.
