Alright so there's several places to start critiquing this app, but I'm going to start with the backstory. The backstory is, in essence, the backbone of a character - it forms the spine of any good OC. Whilst the 'spine' is not outwardly 'visible', without a good or functional spine, the character will fall onto the ground and flop, so to speak. Every character needs a good backstory to be a good OC - but what are the makings of a good backstory?

- Self-Contained Realism: Does the backstory function within itself? Disregard every other part of the character and the application and look solely at the backstory. Does it make sense? If this backstory was written into a book, would you accept it? If it was your job to review said book and find flaws within the backstory, where would you find the flaws? A good backstory functions on its' own as a realistic (within reason) 'novel'. I say 'novel' because not every backstory would be suited as a novel, but rather, it should be able to be a novel or short story. It should, in essence, make full sense without questions left unanswered in itself. We have to take a look at the context here - it's a Danganronpa OC, so it can stretch the boundaries of realism - but even in Danganronpa, your character's backstory should make sense. It should not have unanswered questions, plot holes, loose ends or ties, or feel 'empty.'
Let's start with looking for the flaws in Hososha's backstory whilst ignoring everything else about her for now - as in, let's start with the self-contained realism of her backstory.

Kidnapped by an unknown culprit: Who is this culprit? How did they kidnap Hososha? What did her parents do that lead to her kidnapping? Did they not keep an eye on her as well as they should? Did they tend to be out of the house working often? You say they were poor - why would a poor child like Hososha be kidnapped? Remember, a kidnapper is not someone who randomly picks up children - that would be far too dangerous and risky. They plan their targets, searching for people they known they can make the most money out of, if making money is their goal. Kidnappers would be far more likely to target a middle to upper class home, one especially that would try to avoid a scandal - so that they can be assured they would be paid the ransom, and so they could be assured the issue wouldn't be dragged into the news too much. The ideal kidnapping target is an upper-class child with wealthy parents that don't pay enough attention to their kids, which the kidnappers can insinuate to help push for no media contact. Why, then, is Hososha kidnapped by them..?
She is sold to a terrorist organisation named Aleph: What are Aleph’s goals? Why do they want Hososha? What is Aleph’s relationship with the kidnapper of Hososha - does the kidnapper regularly bring kids to Aleph? Why does Aleph not have it’s own supply of kids, are they a small organisation? Remember, Aleph is going to have to house and feed and spend money on training Hososha, if that’s their intention. They need to feel assured this is worth it - raising a child is pretty damn expensive, and if the kidnapper just brings random children to Aleph, then Aleph has a lot of children to raise. There’s a lot of questions here, and this is arguably one of the most pressing parts of her backstory. All of this should be fleshed out far more so we can understand why any of this is happening, otherwise it breaks away from the realism and demonstrates a less thought-out character. I recommend overhauling this part entirely and figuring out a better way for her to get into the terrorist organisation. If you still wish to keep the kidnapper, you should formulate a much clearer idea of what’s going on there - I have no idea what relationship the kidnapper and Aleph have, and that should definitely be established, because kidnappers selling random poor children they picked up off the street to terrorist organisations is pretty damn unusual. Also outline Aleph better - what do they do? What are their goals? Why do they exist?
Tataka/Hososha was trained as a killer: Extrapolate on this. How do they train her as a killer, what kind of techniques do they use to do this? All this is important information to build on as it helps paint Aleph as the bad guy (which they should be painted as) and helps shape Hososha’s personality, although we’ll get to that later. And the important question still remains: Why Hososha? Why is she being trained, out of all the poor kids in the entire world? Why was she kidnapped specifically and why is her food, water, and living costs being paid for as Aleph evidently houses her (since she has nowhere else)? Why do they think that Hososha can be trained into a killer? Essentially, the questions we boil down to here is ‘why is Hososha worth the incredible amount of resources it takes to train her?’ and in fact, ‘why Hososha at all? Why has Aleph paid for a poor, uneducated 2 year old girl? Why not kidnap one themselves, if they’ve got enough resources to train her into a killer?’
Aleph suppressed her emotions as much as possible: This is a common line of thinking for people writing about ruthless killing groups, but I have to say, I don’t think Aleph would do this. Have a look into terrorist interviews on media and the like - are terrorists cold and emotionless, killing machines without an aim? Do terrorist groups truly breed these kinds of people? Or do they instead create people who are so emotionally and personally invested in what the terrorist group strives to achieve that they can abandon their sense of morality and kill others to get there? Terrorists are very often not cold and emotionless machines - rather, they are passionate, fighting for a cause they dedicate their lives to, fully prepared to do what it takes - even if that results in ‘unfortunate casualties’. This is also part of why I say Aleph’s aims need to be extrapolated upon, to help clear all this up and make it believable in the context.
Tataka’s tasks consisted of killing a certain high-importance target: I have problems with the targets listed. This is because Aleph isn’t fully fleshed out properly - so their existence is just… publicly know, and big businesses oppose them in a way that’s significant enough to dispatch an assassin to kill their CEO? Where is Aleph situated, anyway? Why can’t the government deal with them? This part will be solved by addressing earlier parts for the most part. However, it is a direct contradiction to what happens next.
Tataka not killing Haira: This is one of the biggest issues I have with the backstory. If she’s been trained as a killer her entire life, a cold, mindless, calculated machine… then why doesn’t she kill Haira? Do you really believe one moment of doubt is enough for Tataka to suddenly abandon years of conditioning and essentially what I’m assuming is brainwashing? All for… a girl that’s the same age as her? I really don’t see why she doesn’t plant a bullet through Haira’s head to ensure her own safety and then go back to being Aleph’s killing machine. She needs a better, more plausible reason for this - does Haira remind her of a friend she had whilst growing up under Aleph’s training, perhaps a friend that was brutally murdered by Aleph as an example to others after she tried to escape? That would cause Tataka to pause - to recall her friend - to call into question whether what she’s doing is truly, ultimately worth it.
Where does the music come from?: I’m at a loss here - I have zero idea where their musical talents come from, or at least Hososha’s as I haven’t read Gisei’s app, but - Hososha has been trained her entire life to be a brutal, cold killing machine without emotions or remorse, a simple tool used to kill others. It’s been expressly stated she doesn’t know much basic schooling because Aleph neglected that - so where does her drummer talents come from? How is she, in fact, good enough to parade around as the Ultimate Drummer at all? Where does this extreme drumming talent that’s enough for people to think she’s an Ultimate even… come from? Logically she should have zero idea how to play the drums at all. This is a major point that needs to be addressed.
Why can’t Aleph find her?: Another important point. I simply cannot make out whether Aleph is super powerful (they take out business CEOs and anyone in their way without being dismantled, and I assume they’re situated in Japan which would be an insanely hard place for a terrorist group to thrive), or whether they are super weak (they resort to having poor, kidnapped 2 year olds as their ultimate killing machines, wasting resources on a gamble that might not work out, and their conditioning isn’t good enough to withstand Hososha being told to kill a girl her age). Why can Aleph not… find Hososha? Do they really possess enough skill - two 15 year old girls whose ultimates don’t particularly relate specifically to this - to avoid the eyes of a massive terrorist organisation? Especially since Hososha and Gisei are both the same age as the missing target and missing assassin, will be the exact same builds as the missing target and missing assassin, have zero past that anyone knows of and constantly travel as if trying to evade capture?