I recently read the book Eccentric Orbits about the Iridium comms system that was a lot like this (recommended by the way). One of the technical issues that was mentioned in it was that the satellites had to correct for the Doppler shift in the frequencies they used to talk to each other because of the high relative speed they were traveling at. I wonder if these satellites have a similar problem or if lasers are so directional they can afford to not be too discriminate in what frequencies they accept.
Generally optical comms systems in space are not affected by Doppler shift because of their modulation scheme, not the directionality of the beams. They tend to use some type on-off keying (sometimes called OOK) where data is encoded in the pattern or duration of fully on and fully off laser pulses. If there's a variation in the frequency of laser light being received, it'll still just register an on or off signal on the photodetector on the receiving spacecraft. Radios, on the other hand, use modulations that rely much more on the actual frequencies and phases of the radio signals they receive, making frequency shift due to Doppler a much bigger factor.
The radio encoding schemes are more efficient in a bits per Hz-of-EM-spectrum sense, but optical systems have the advantage of being at such a high frequencies that even "inefficient" coding schemes can reach very useful datarates.
Forward and back looking lasers would have minimal speed difference, side laser links don't appear to be at extreme speed differences according to these hypothesized connections:
https://youtu.be/QEIUdMiColU?t=132
