These aren't (just) masks (spoilers ahead).
On a quick note, there is no reason for me to write this. This is simply a way for me to set my own understanding of the finale straight, as well as, maybe, clarify some details about Jax's character. The conclusions here, as the opinions provided, aren't revolutionary by any means, aren't the ultimate truth, and were written for my own entertainment. I do hope, my words do some good to someone though
I don't think these "fake Jax" characters are as simple as just masks. Let's go one by one.
The piano Jax is the closest we SEE in this scene to a "real Jax." Not only we saw her (and Pomni) sing "Daisy Bell" in episode 6, that is the song that Jax is playing on the piano in this scene. But it would be foolish to say that by looking at the artistic Jax we saw the entirety of the "real Jax;" she is way more complicated than piano and singing.
The "maid Jax" is a mask. It is the mask of ironizing and ignorance. When Kaufmo abstracts in episode 1 and Jax pretends to be calm and unfazed, when Jax tries to ignore Ribbit in the finale, it is the mask that she turns to. It is also the weakest of these masks. As we seen in episode 9, she does care. She nearly cries for Kaufmo, and the "not caring for Ribbit" bit is hardly believable to anyone, including Ribbit, with whom Jax gets into a shouting match. This mask is far from Jax's real identity, and is simply a first line of her self defense mechanism.
The "Cartoonish Jax" is the representation of lies that Jax told herself about the circus. While she merely pretends not to care, Jax fooled herself into believing nothing is real, as seen by the scene in episode 8.
"This is real." That was the realization that his actions had real consequences. Before this, Jax has seemingly convinced that she was in a video game or a cartoon. There may have been cracks in that worldview, but it had mostly held, until that moment. Suddenly, the damage done by her to other turned out to be real. Sure, in the end the all turned out to be brainscans, but their pasts were still real, as were their relationships. The fact, that this realization was such a revelation for Jax means (to me, at least) that it may have started as a mask, but it became a keystone part of her worldview regarding the circus. The mask was glued to the face, although it proved possible (to Kinger) to tear it away from the face, even if the action, or the consequences to Jax's psyche, was unintentional.
The final of the masks shown was the "cruel Jax." On occasion, Jax could be open and honest (if not outright nice), for instance when discussing the fear of corn in episode 6. But this, to her, seemed like a weakness. I don't think I need to explain this, so I will skip to the main part; she overcompensated for her opening up to mom and Ribbit by turning to cruelty. Also nothing new, but just as practice makes perfect, so does acting in a particular turns defense mechanisms into habits, and masks into personality traits. Pushing away Ribbit was a horrible reaction to fear of this being held over Jax's head (which is directly said in Ribbit-Jax shouting match), but cruelty to Pomni, attempts to push her away in episode 6 after the gun fight was more of a habit. Sure, there was a defense element to it, but the phrase "I [would] probably forget about you," seemed almost rehearsed. It wasn't, but it was coined by months, if not years of pushing people away and being cruel to others. Jax didn't even realise what she said until Pomni turned around and almost shot herself. This is because the cruelty mask became a part of her personality. A way to hide "her" and present a profile of "him." Profile of cruelty, ignorance, and denial. In the end, it became the only thing that everyone saw, including Jax!
Luckily, people are more complicated than their masks and defense mechanisms. Going back to the example from episode 6, when Jax saw Pomni's reaction to HIS words, SHE then followed up with "[...] can't take a joke [...]" which is an indication that the real Jax was never fully covered up (JUST TO BE CLEAR, I am not saying that all men are cruel, I am saying that the male cultivated in Jax was of the toxic kind). Despite the habit of cruelty, and the distorted world view, she was still there to, on a rare occasion, remind the masks (and herself) of the rights and wrongs. She did learn from Ribbit's and Kaufmo's abstractions, that losing people you're close it is far, far worse than showing vulnerability. In fact, after this moment (when Pomni throws her pistol at her) Jax ends up showing vulnerability, when she displays her real feelings regarding herself to Pomni.
Above, I tried to show that those aren't simply masks, but genuine parts of Jax's personality and even (to an extent) identity. Pomni wasn't looking at Jax's defenses, but, in at least two instances (cruelty and piano), the real Jax! It just so happened, that these traits weren't determined by genetics, or education, or social status, but by Jax herself (with the "help" from her mom). Jax chose to cultivate cruelty in herself, until it largely replaced her, and added covers of ignorance and denial of reality on top.
Which brings me to the point that has already been made several times by others (albeit, in different words): Jax chose this path. She chose to lock the best of her parts behind chains while expanding upon her worst traits to defend against others. But those mechanisms consumed her real self, leaving no room to escape. Despite this, Jax was given several opportunities not to descend down this path. In Ribbit's room, most obviously, she was offered a plan to settle issue with her identity and childhood, but she rejected it, instead opting for the alternative discussed above.
When that proved a deadly path for others, Jax doubled down on this road with Kaufmo and Ragatha, pushing them away as hard as possible, to protect not just herself, but also them. When that proved to be counterproductive to the utmost extent, it simply convinced Jax that this road was her real identity, with everything else being locked away further for others to never see.
This is where the Pomni factor enters the fray. Pomni genuinely tried to reach out, putting Jax into an internal conflict. Kinger's revelations in episodes 8 & 9 added on top. Jax realised where the road was leading. The locked away "real Jax" started fighting back. This is my explanation for why Jax approached Pomni after she and the others began rebuiding the circus. However, the worldview that has formulated after 2 abstractions (Ribbit, Kaufmo) and 4 ruined friendships (Ribbit, Kaufmo, Ragatha, and Pomni) gave one last fight. When Jax said "You're not supposed to care," she was sincere. In her worldview, she didn't deserve to be saved. Not after everything. The worldview won, after which, it was too late to do anything.
Jax's choices in the circus let her to pick the worst path and then double down on it. But when she realised it was the worst way to go, she didn't found the strength in herself to turn off that path and instead of accepting someone else's hand to go on a better road, she decided that she was underserving of help, spiraling down to abstraction. The moral is clear: accept help and don't abandon yourself in despair and thoughts that you are unworthy of something. Take the help now, because there IS someone who cares and doesn't want to hear you say "I don't want to go."
One more thing. As I was wrapping this up, I realised that the phrase could be interpreted with double meaning. Jax never wanted to abstract, she didn't want this to be irreversible, but even now she might (I can't say for sure if she means it, it's up to interpretation) be refusing to accept Pomni's help, and I don't think this is just a habit of pushing people away (this time). Jax thinks that she deserves this end and, while she doesn't want it to all end like this, she also has no wish to subject others to her presence, if she chooses to accept help. In my opinion, she thinks wrong, she (and anyone else in a similar position!!!) should accept help.
This is a note to take: when you push others away constantly, it allows you to be consumed by the worst doubts and thoughts, so that even the threat of the point of no return may not be enough to accept help. And while it may be impossible for you to "pull yourself up by your bootstraps" alone, you can allow others to pull you before its too late. You are worth their efforts. Please accept people into your life. Going down the path of rejection of, and cruelty to, others, will only bring the point of no return closer, whatever it may look like in your case. But if you accept others, they will help you avoid, or leave this path. And once on a good road, you can stay there, going along with your life, or helping others find theirs. This is why YOUR LIFE SPECIFICALLY is worth so much, because without it, all lives around lose. Even if you feel unworthy, others can make you feel better, help you get out of the moor and onto a better path, so that you can pass that newly earned worthiness on.
This was a pretty chaotic write, one that could have been better and shorter. If you read it all, and it did something good, be it uplifted spirits or a new glance at Jax's persona... I am as delighted as I am surprised. I don't claim to know all the answers. I DO NOT know all the answers. I write what I think is right, and the let you be the judge of my words. All criticism is welcome