This whole introvert/extrovert label drives me a little crazy, just like almost anything that attempts to put people into boxes.
Humanity really needs to get past this foolish notion that things are black and white instead of the real shades of grey.
I probably straddle the line of introvert/extrovert. People tire me out, and I recharge in solitude like an introvert, but I'm also quite gregarious, and need to be around people getting a regular fix. I could never work solo on anything. I couldn't cope in a role that doesn't involve at least a handful of meetings a week (though they have to be legitimate, because I hate wasting my time in meetings and get easily bored in them).
I'm probably close to what OP was talking about, and it has certainly been integral to my progression to staff engineer, but like you I disagree with the premise that you need to be particular ways to make progress in your career.
While all of the staff engineers I work with operate at the same kind of level, I'm surrounded by staff and staff+ engineers of every stripe. From extremely introverted specialists in particular fields, all the way to extreme extroverts focusing on cross org collaboration and consensus, and every possible combination of behavior in between. That diversity is essential to our effectiveness.