most laser systems get close to diffraction-limited divergence, which is governed by the size of your optics. vacuum vs. air affects it, but the effect is so small that you need sensitive instruments to detect the effect

https://en.wikipedia.org/wiki/Gaussian_beam#Beam_waist

the divergence angle is inversely proportional to your aperture diameter

https://en.wikipedia.org/wiki/Airy_disk

in theory by putting a bunch of laser emitters in solar orbit and operating them as a phased array you can make an aperture the size of the solar system. 1.22λ/d at, say, 400nm and 2 astronomical units of diameter is about 1.6 attoradians of divergence; at a radius of 4.3 light years (the distance to proxima centauri) this works out to an airy disk focal point of 66 microns. optical phased array lasers have been demonstrated https://en.wikipedia.org/wiki/Phased-array_optics but nobody knows how to make one out of satellites yet

i've only glanced at the proposal https://arxiv.org/pdf/2309.07061.pdf and they're proposing 4.1-meter-diameter 3.6-gram probes, which would allow you to use a phased array about a million times smaller, about 5 million km, 13 times the distance to the moon. i don't see where they're proposing how they propose to beam 100 gigawatts onto the probes so i don't know if this is their proposal

dispersion, by contrast, which means wavelength-dependent indices of refraction, doesn't affect lasers and doesn't happen in a vacuum; probably the person who mentioned it was using the wrong term by accident and meant divergence