What are they based after?

Well that is easy, they represent commedia dell'arte, a type of italian theaters, each character covers their face with a mask, and each one of them represents a role.

Those roles are their code names, Il Capitano, Arlecchino, and such.

However, there is something that I want to point out.

There is a certain role that is not represented in it, and that's actually reasonable.

Innamorati, the lovers, the only characters that do not have a mask. And they represent Aether and Lumine, as they seek to meet one another once again, of course, removing the idea of it being romantic of course.

The Fatui Harbingers alongside Aether and Lumine are basically a big Italian play.

In some cases, they ask for the help of the other characters in the commedia dell'arte to send their messages to one another, or at some points, even involve them in their help to meet one another, and whenever they meet, they are unable to exchange words with one another.

Something unrelated but pretty interesting is that, the Innamorati are usually the children of either Pantalone or Il Dottore, but it may not always be the case, in certain cases it is possible for them to be someone of interest as... they may want to get into a relationship with the female Innamorati or they raise them even though they are not their father.

Now, what if we try to predict how each of the fatui are going to act towards the Traveler based on how they act in the commedia dell'arte?

Of course, this would just mean that, according to the trivia of the etymology of each of them, would mean that Pierro gets NTRd by Arlecchino as in commedia dell'arte Columbina is the Pierrot's wife lol (That being said, they could also just be good friends).

However, keep in mind that, due to the characters being of the Italian theater, it is possible that Pierro is not Pierrot, but rather Pedrolino. His character is the definition of adding more wood to the fire, as he wishes for the Innamorati to get together, not because he wants to, but because he sees the chaos it may create to be fun. In a case, pretending to be another person to convince Dottore of them needing to be together.

Expect a character to appear and turn out to be Pierro.

He is double faced, which could explain his half mask, as he plays as devil's advocate.

Il Dottore alonside Pantalone are basically the main threat, in the commedia dell'arte, they can either be friends, a mentor of one another or competitors, one thing that I want to note, is that his personality alongside his relation with Pantalone seems to fit the description of what the wiki says. That being said, there is also hint of Dottore characters being cucks.

Columbina is actually someone who helps the Innamorati in commedia dell'arte, there really isn't much information aside from that when it comes to connections between the characters that hasn't been mentioned before

Arlecchino, is a character that goes on its own, usually challenging Pierrot. Which could hint to defection so long as the ideas of the Fatui do not connect with what she wants, but at the end of the day, this is theorizing based on the original source they based things after.

Pulcinella, well this one is interesting, as a stock character, there is a lot that can be done with him, froma  cunning thief, to a pervert, there is something that any of them have in common, and thats the desire to climb the social ladder. He is usually seen as the savior of the people, however, they are selfish and do everything so long as they have personal gain from it. This makes me theorize that, once we meet him in Snezhnaya as he is the mayor, he will act friendly towards us, we will pretty much see nothing wrong with him, and will be beloved by the people, however, we will attempt to remove that mask he has to the public, we gain the hatred of the people of Snezhnaya, which leads us to, yet again, be in trouble and become wanted in there, from there, we end up convincing the Tzaritsa of whatever she is plotting, or we help her with it, and she then gets rid of Pulcinella. He is a schemer, who has a false persona to the public, and works quite well as a mayor who wants the best for his region, but in reality is absolute scum.

Scaramouccia, well honestly, I didn't find much information about them. But there are few certain personality traits that seem to be quite similar to The Wanderer. Those being boasting and cowardice. Boasting as he was being boasted by the saged as someone equal or superior to Rukkhadevata, and cowardice due to how he then tried to flee from Dottore alongside how he was about to lose he pleaded.

Ok, so for Sandrone don't have anything to say that has anything to back it up, instead, I want to theorize based on a certain line I read. For Sandrone, I think that her character will be based on the fact that she is going through denial of the death of her family, thinking of herself as her husband, the puppets and such are her way to try and make her husband and children come back from the dead, by replacing them with puppets. This whole theory came to me after reading this "Sandrone and his family arrive at the train station from the imaginary village of Bosco di Sotto." The word "imaginary" struck very deep with me, as this is actually something I actually saw done before (Jae-Heon from Library of Ruina) and I want this to be done yet again.

La Signora, a character in commedia dell'arte, who I can't find anything about in the wiki. In a way, her demise could be attibuted to this line. "A common lazzo of La Signora is to have a fight with another woman, as she is very proud and often ridicules others."

Pantalone, who often appears at the beginning of the story, doesn't seem to do so phisically in the game... Except the Goth Grand Hotel, in commedia dell'arte, the story begins with an event caused by Pantalone. Aside from that, expect for the character to pin for a younger looking character... Yeah thats in the wiki of the stock character.

Tartaglia, oddly enough, he is sometimes one of the Innamorati, so if you wanna make a fanfic, you can use this little speck of information for your own fanfic. Aside from that, there doesn't seem to be much information about what his role in the story is.

Il Capitano... Man this hurts, but it seems like he may be an actual fraud if he actually turns out to become accurate to the stock character in commedia dell'arte. Either way, expect him to either be someone who will stand by your side because he wants you, or betray you because you're loosing, atleast if he turns out to be like the stock character. Expect him to be like King, Mr. Satan, Buggy and all of them. (Mika's mention of him does not help at all either).

Please for the love of god Capitano, don't end up being like your actual source.

There are so many red flags, the hefty amount of nicknames, the fact that he has such a huge reputation, the fact that he peacefully departed in Mika's mention, the fact that he can either be 1st or 10th which can be used as a gag for people confusing the numbers. Jesus Christ.

Like there are so many ways this can go, and many that I can see but are at the same time so unrealistic. Him being in actuallity a small boy in a mech suit, an actual fraud, someone who holds those titles and is actually what he is.

Additionally, the characters are divided as such.

Zenni, servants and characters that usually help the Innamorati, those being Arlecchino, Columbina, Tartaglia, Pedrolino and Pulnicella, although the last one is out of personal interest.

Vecchi, rich characters usually against the Innamorati, those being Il Dottore and Pantalone

Il Capitano by himself is actually a group of characters which include Scaramuccia and La Signora,

For Scaramuccia, they are depicted to be unintentionally helpful towards the Innamorati. In certains cases, can even be depicted with puppets, Punch and Judy being an example.

La Signora is actually a female version of Il Capitano in commedia dell'arte, but with a different purpose.

Il Capitano in commedia dell'arte has a lot of showy nicknames. Given that he is the only character with his mask completely covering him of the Fatui, in the plot of commedia dell'arte, upon uncovering it, he shows humility and panic.

I've come to really think of various ways this can go. For example, once he gets to Natlan, if he is defeated by the archon, upon uncovering his mask, he becomes the opposite of what he acts, as a reverse per say.