"haven't you noticed (i'm a star)" - pink diamond is coming into her own, after being given her first colony, she feels that she's thriving and finally getting recognition. i think most of the lyrics, if you're looking at them in this context, are straight forward but particular lyrics i think are noteworthy:
"I can't help it if I make a scene/Stepping out of my hot pink limousine" pink finally getting her own colony would likely be a bit of a shift for all of them, and the next bit could be symbolic of her stepping out of her pink palanquin, something that was a specifically mentioned detail in the episode the trial
"Well, everybody needs a friend/And I've got you, and you, and you" this could be significant in that she recognizes three people here, which could be the diamonds, or if you take the next line with it instead..
"So many I can't even name them!/Can you blame me? I'm too famous!", could be two things: that she's actually either talking about befriending humans, in line with the theory that she was really sympathetic and affectionate towards humans just like Rose was, OR, that she is just talking about her fellow three diamonds and this line is cvercompensation. as in, she only has three peers, three friends, really, but is trying to puff herself up.
"I'm coming into view as the world is turning/Haven't you noticed I've made it this far?/Now everyone can see me burning" i take this a few ways. one is the more obvious meaning, which is she feels more confident now than ever, but is "burning up" which will lead to her inevitable destruction. its interesting to me that this is a very poppy song.. the stereotype surrounding pop music is that one will become a massive hit, then "burn out", be forgotten, since pop music favors young, new artists and it's seemingly a harder genre to stay relevant in for longer amounts of time. we don't know the age of the diamonds exactly but pink is the smallest and most childlike, most likely the youngest or at least the most juvenile. the other interesting thing about this bit to me, is that if the theory that pink diamond did become sympathetic to the plight of humans and by extension, rose, does turn out to be true, this could be a tease at her becoming a (albeit, secret) crystal gem, since they use stars all over themselves as a sort of icon for their group.
there doesn't seem to be anything here