Yup, I think that's the implication of the "space laser network". The plan for Starlink has been to have laser crosslinks between the satellites to provide coverage in places where the satellites can't directly see a ground station.
Forgive my ignorance but I don't understand why it's an unimaginably difficult task. The satellites are operating in a vacuum with no weather interference or anything and have line of sight to each other. I would think that it should actually be easy to pull off, and actually should get easier at scale since the distances between individual satellites would shrink and would be easier to align the laser links.
Some people have speculated that laser links within the same plane (where satellites are stationary relative to each other) are working and the others are not.
Both, they have two sets of orbital paths at roughly 90 degrees to eachother (I'm just eyeballing it, it's probably not exactly 90). With more sets if you count the satellites in polar orbits.
Though they could, if they needed to, only connect to the satellites flying at low relative speed.
I see it as one of those enormously difficult and yet practical things, like photolithography. The human sweat to produce this system is surely measured in decades, if not centuries depending on whose effort we want to count.
If they wouldn't have been able to pull it off why would they have launched the satellites? I don't get why people constantly underestimate the ability of Elon Musk companies to points beyond what is reasonable. They're not going to just do something that's very likely to fail. That'd be completely uneconomic and unaffordable.