Remember that the only reason a laser works for this kind of link is that it is very highly collimated. The light scattering from the receiving satellite is diffuse so the intensity will go down very quickly with distance. It might be observable with a suitably large telescope, but I doubt it would be practical.

So you have a reflection off random bits of equipment followed by a trip through most of earths atmosphere? That doesn't sound easy at all - and they could choose wavelengths that won't make the trip well if at all.

I guess if you got an observation platform up closer that would help.

More like farther away. Put a spy satellite in a high orbit like traditional satellite internet and it'll be able to see half of Starlink simultaneously with essentially no distortion.

If they were strongly encrypted there may be no reason for a nation state to observe the intersatellite links, but I wouldn't expect this at least for the near future since Elon's focus will probably be to cut corners to get the absolute best performance possible.