Giftedness, or any sort of talent or inordinately high degree of expertise, is positively correlated with perfectionism—the higher the talent, the more pressure to perfect it.
Therefore, gifted children tend to struggle with anxiety and depression, not more so than other kids, but for different reasons, generally though not always. Often, gifted children are idealized, especially in families of high and low socio-economic tiers. On the higher end, the children may feel pressure to continue a family legacy; on the lower, to begin it. Their thinking becomes zero-sum, wherein the world is divided between winners and losers and it's impossible for everyone to prosper. While there's some truth to that mindset, considering one's circumstances (including external pressure), the social division may feel exaggerated for the gifted kid, who believes mistakes to be death sentences.
One talent, whatever it may be, can't save a family, even if it does make them rich. So, the gifted kid may struggle with not only their limitations but those of the world, too. Parents often ask me how to help support their gifted kid as they try to grasp how depression and anxiety tend to manifest in them. Parents often say things like, "I'm only depressed when my basic needs aren't met. So, I don't know what to say or do with my kid."........