DD still doesn't really know.
I mean, she knows that she's gifted, and she knows (intellectually) that she is "more gifted" than most of her gifted peers-- both same-age (because they are doing work she did years ago) and academic peers (who have to work much harder than she does to earn the same grades).
She only knows a few other PG people. Most of them, she doesn't "click" with on a personal level, but the handful of EG people she likes pretty well. Most of them are 1-4 years older than her, so they tend to have similar interests and academics going on, so a lot in common...
One problem with having a HG+ child that doesn't KNOW how unusual they are is that they tend to measure themselves in ways that are really unhealthy since they lack external rubrics for doing so... other than perfection.
My DD is refreshingly unconceited, which makes her extremely likeable. On the other hand, she is far more insecure than she probably ought to be. She tends to assume that she's "nothing special" by default, even when others treat her like a mascot/poster child.
If anything, I think that my DD as an adolescent prefers to NOT think about being something of a singularity. She has avoided considering it, I think, because it makes her feel very lonely.