Being an extrovert does not mean happier. Yes when we think about being social at specific times I want to be outgoing.
When my daughter had fundraisers for her school they did it at a resort in Orange County. Most times I did not care what car I drove but pulling up in my old truck to the valet stand made me self conscious. But it was a specific time.
Most of my best friends are outgoing, charismatic, extroverts. But I know their struggle and heart to heart talks. They are not quantify happier. They live life a certain way and at times their personality and skill shine. I can say the same for me just at different times and places.