It really depends on the General Audience of the story itself.
Stick with extrovert protagonist if you want to gain International English reader. It's always the best for most people who never being secluded while suffering depression. They always criticize Introvert as "Loser" and "Stupid Human Being" and then gave less star on review due to that.
I have read lots of review on Novel updates and they criticize lots of them due to protagonist for being loser, not because the story itself have bad Grammar or other.
So just use Confident extrovert that were quiet or talk like confident gentlemen if you want to write stories. It's always how hero was potrated since ancient times, and it still works today.
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Usually Introvert in JP LN harem story is always introduced as Introverted Jap boy Hikikomori with no friend at the first appearance. But, after suddenly gain "MaGic" and Having Love interest, Harem, and Gain friends like Extrovert.
If we're going to ignore the bullshit in the plot and just focus on protagonist interaction, it's basically "Extrovert" that became suffer in loneliness due to being incapable to gain friends for "some unknown reason", and then the protagonist gain his old extrovert personality back after being able to "gain girls" and friends. That's my analysis on the protagonist itself.
In my opinion, It's basically trying to give dream for Jap loser Hikikomori for being able to talk and interact with other easily just after magical extraordinary event, No matter how unrealistic it is.
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If we want to look actual introvert, take a look at Shinji from Evangelion. Even after all extraordinary status he got and he gain friends, his depression and lonely introverted act is not cured.
And Asuka is still showing extroverted personality even when being Hikikomori in her friend house while playing games.
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The conclusion is, both Introvert and Extrovert can be good as long You out effort into writing them.
But, if you want to gain more audience positive response, always see what is popular on the novel scene and just use confident extrovert as a basis in the protagonist.
They hate loser beta male MC, always.