Parents of (formally tested) gifted children, or parents who are gifted themselves

My son is just 2 years, 4 months. His pediatrician witnessed him doing some basic reading, and using perspective words (almost, barely) and encouraged me to have him tested as gifted. I’m not going to pretend I wasn’t immediately beaming with pride - of course I was!

Now, my son is ALSO one of the most hyperactive children you could ever imagine meeting. To the extent that I previously thought he may be sensory seeking or have some other issue (he’s since mellowed... a little). So to test him this young, what would the real advantage be? Has anybody gone through this?

I tested as gifted because my mom ... I think she just wanted to be able to brag? All it did was put a label on me, and a justification for her to push me. I am not aware of any advantage it had scholastically, I never moved up a grade, and college admissions certainly don’t ask if you tested as gifted in elementary school. In high school, everybody got the chance to take AP classes so nothing special there.

I could see it being a good thing if he was a relaxed little boy, and I felt like he could skip kinder I guess? But he probably needs that year to mellow out more (still early to make that call).

What advantages would there be for him? What opportunities would it open up for him? Or would it be an added stigma with no real benefit? I’m not sure and would like some opinions.