Reading about terminal degree's student winning a contest at age 14 made me think back to my own piano-playing days and the types of performance situations I was exposed to. One of the strengths of my piano teacher (the only one I've ever had, from ages 6-18) was her ability to maintain high standards and a rigorous level of teaching in the absence of many external motivators like contests. I did, on occasion, participate in the statewide music judging that would have qualified me for state piano ensemble had there been such a thing. As it was, it simply provided a little performance opportunity. And there were more and less formal recitals of my teacher's students as a group, held in her living room.
I didn't get much practice dealing with things like performance anxiety, though, because all of those outlets were so low-stakes. Once I got old enough and skilled enough to play somewhat challenging music, anything I played after the 6-year-olds' plunky tunes was enough to make me feel good. It was only when I started singing - auditioning for solos in school choirs, or, later on, performing in a more extended way in front of an audience - that I developed a good sense of the internal and external standards by which I could gauge my own performance. This happened partly because I was older, more musically experienced, and had a clearer conception of what I wanted to sound like before I started singing. But it's also because I just had more numerous opportunities for self-exposure.
The process of learning to deal with that kind of exposure is ongoing, especially because I constantly have to adapt it to new situations, both musical and otherwise. Simply performing the same piece in different physical spaces requires a mental and aural adjustment - it's still challenging for me not to get nervous, for example, when singing in spaces where I can't hear myself very well; that cushion of reverberation or feedback is somewhat of a security blanket. Job interviews, conference presentations, etc. require the same sort of self-fashioning and self-reassurance in public; what I'm learning from performance is the ability to hear in advance what I want to sing or say, and to use my technical know-how to make that happen.