My present understanding is that starlink satellites with lasers are not designed to communicate inter-plane. Each launch of starlink satellites is put into exactly the same orbital inclination (53.2 degrees or the more rare near polar orbits now launched from Vandenberg).
In the weeks and months following their launch they spread out into an extended line all following each other in the same plane. Plane change maneuvers are extremely expensive in delta-v for any satellite and are generally avoided unless absolutely necessary. Best conjecture is that starlink satellites' on board propellant for hall effect or ion thrusters (or whatever they're using that has an ISP above 3000) is used almost exclusively for thrusting prograde to maintain altitude.
If you view a launch of 45 or 50 starlink satellites in a live animated satellite tracking application, based on their TLE orbital data, they all follow each other in a line. Satellites in the same line may be using inter-satellite lasers to speak to the unit immediately in front of it, and immediately behind it, forming a conga-line like network of linked satellites until they get to one that is generally above a starlink earth station/terrestrial network facility. At which point the traffic is transferred.
Starlink has recently made service available for purchase in Nunavut and all of the other high-latitude areas of northern Canada, which means that they clearly think they have sufficient (82 degree plus) inclination sets of satellites and inter-satellite links working to provide service in an area that definitely has no terrestrial fiber or starlink earth stations.