Most data and internet from pole is via ~4 hours of DSCS a day, ~4 hours of skynet (slowww...) or when TDRSS decides to gives South Pole time (but in small chunks of time).
I usually try to ssh in my experiment at Pole the start of DSCS time, which unfortunately can be in the middle of the night for me.
But there has been nowhere near enough money available to do something like set up a pair of molniya orbit satellites with long apogee dwell times over the center of antarctica.
Assuming that the topology will be additional highly-inclined/polar orbit starlink satellites, communicating with each other in a laser chain, this will be dependent on starlink setting up earth stations near fiber somewhere in southern Chile, Argentina or in South Africa. Or south australia, tasmania, new zealand.
Now that I think about it though, the Starlink user terminals likely won't be able to survive the harsh winters at the poles. -30 deg C and low tolerance for high winds means this would be tough unless some type of non-obstructive sheltering could be provided.
Even if you maintained multiple $1.25 per minute (or $5 per megabyte) Iridium links, operating 24x7x365, it would be a teensy tiny drop in the bucket compared to the total budget of the station.