While some of the satellites do have point to point laser links for communicating directly with other satellites in the constellation, it's not widely utilized yet, and all communications are ground station to satellite and back to base station.

https://caseyhandmer.wordpress.com/2020/09/23/starlink-packe...

It's unlikely that anyone's traffic is passing through multiple satellite links at this time, but that may change with higher elevation orbits serving states like Alaska.