My 2e pg ds7.5 fits a lot of these descriptions and we've been in similar shoes since preschool too. He was misdiagnosed with ADHD and other stuff. I can't tell you the number of times I had teachers or various therapists say he shows ADHD-symptoms.

Ds was in two private gifted schools for pre-k/k and displaying similar behaviors. I can say that the behaviors you are mentioned are most likely directly related to the school setting.

My son has had some testing, but he hasn't fully cooperated with it to get a test score that is more aligned with his ability or performance at home.