There is a common image of the gifted person as socially awkward, intensely focused, emotionally sensitive, and a little hard to be around. But how much of that is actually supported by research and how much is just cultural mythology built around a few famous outliers?
The overexcitability framework is interesting but it gets overapplied. Not every gifted person fits that profile and plenty of non-gifted people show the same traits. The most consistent finding in the literature is elevated openness to experience. Beyond that the personality picture gets messy fast.
The stereotype probably comes from the most visible gifted individuals rather than the full population. High giftedness is rare enough that most of the data comes from small samples or self-selected groups. That makes it really hard to generalize. The heterogeneity within gifted populations is probably bigger than most people assume.