Personality systems like MBTI, is based on four ratios, each is between two facotrs.
Extrovert <<< percentage%>>> Introvert
And so on..
Now Prophet Muhammed (pbuh) was moderate in everything, the mean value, the golden ratio.
Simply perfect example of a human.
So I think he doesn't belong into a certain type, and I'm assuming because he was moderate otherwise it's very normal for him to belong into a type, he was not a super human, but he was the top human because of his characteristics, exactly the golden mean.
This is what I think, but again even if he belonged to a type, he was the type of a man, although he was a king and ruled by the noble book of Quran, you'd bot recognize him when he was sitting plainly with a group of men.
He wore no crown, sat on no throne, even before prophecy he was known for his -litrally- good manners.
The key for being best, is, the perfect, simple, moderate measure.
Is what I believe after I realised the prophet always picked the easiest choice when he was given.
Summery:
He was not that introvert, "he was closed to his fellow muslims than their own selves"
Not even that extrovert, he used to go to a cave just to think, all alone, before gettig the prophecy.
wasn't just a thinker he was merciful.
And I fon't think he was a sesnor more than an intutive, or a judging more than perceiver.