There is a "hole" in the plasma in the wake of the re-entering Starship due to its shape. They used Starlink terminals to beam the data up to Starlink satellites. Starlink also uses higher frequency signals than older systems and that also helps.
Like how do you move a satellite or satellites to a certain area, at the right time, avoiding other space objects, and then keep them there for 45 minutes during the mission or at least 15 minutes during the blackout zone. I'm sure it takes a huge amount of planning, math, coordination with various entities....
They have 6000+ satellites in orbit. While it may not be easy, it is probably not a huge challenge to plan for one or more to always be in the field of view for this flight.
> As of May 2024, there are 6,078 Starlink satellites in orbit, of which 6,006 are working - https://www.space.com/spacex-starlink-satellites.html