Good question, IIRC the original Eye of Harmony was the nucleus of a black hole that was stored on Gallifrey, and provided power for Gallifrey and all the TARDIS's pulled from that.
However, with Gallifrey in a time lock, is that Eye of Harmony no longer accessible, I tend to think it is locked in with Gallifrey.
In that case, the TARDIS would need its own power source, so this is the "new" Eye of Harmony, but how it got installed post-Timelords, I do not know. Unless it has always been there, which the '96 movie suggests it was.
In that case, perhaps it is a backup power source if a TARDIS ever gets separated from its main source.
That's the best I can come up with
So I take it, the star was really huge in the TARDIS, and we were just looking at it from very very far away, which means the inside of that room has to be the size of our solar system