Starlink could do laser comms with other satellites, probably, assuming they shared positioning information and whatever proprietary laser sauce is keeping their intraconstellation links up.

But their radar link to ground is Ku band, which is already getting congested (partly by Starlink itself!). That’s why everyone’s talking about moving to Ka, despite the worse attenuation and higher cost. Much more bandwidth is available at Ka band, as well.

Edit: I’m slightly out of date, Starlink now also operates at least partially in the Ka band.

Starlink has already demonstrated the capability to do laser communication with a maneuvering spacecraft in a very different orbit from the constellation, during the Polaris Dawn mission. And Starlink has way more than enough downlink capacity for the "staggering" numbers in the article. 85 TB/day is a drop in the bucket compared to the traffic Starlink sees. Starlink will need to expand their downlink capacity in the future, but not because of demand coming from space. Maybe unless space GPUs actually happen.