This seems overly ambitious, and not likely to translate to laser satellite comms links. Remember these sats are in low LEO, so there is at least some amount of non-uniform atmospheric medium to create optical distortion that you wouldn't have in a tightly controlled environment from your link (chip, datacenter, what have you).
Then there's the issue of signal attenuation at distances like these, along with the power budget from the solar panels to ensure that you aren't burning all your power just on laser comms.
I can't imagine these links would be anything more than 1:1 at any given time, at least not at first. Maybe later they might be able to handle simultaneous laser links from 1:3 or something like it, but I highly doubt that's their current capability.
Even some of the best latest ground-to-sat laser comms links are on the order of ~7 gigabits per second. [1] I imagine those are far larger sats than Starlink, and their entire power and thermal budget is likely spent on comms. And the ground stations can be orders of magnitude larger and power hungry in relation to a Starlink sat. Note also that this is from GEO, so you aren't likely having to handle substantial relative movement either.
[1] https://en.wikipedia.org/wiki/Laser_communication_in_space#2...