Salutations!
I've read through some of your work and I've some feedback for you!
Good on you for starting your prologue with some action to get the reader invested. It is never a bad thing to start in the middle of something thrilling.
Now, I know you've heard this twice already but to reinforce its importance: your descriptions are lacking (take heart, they're not horrible, they just need a little more meat on their bones). Remember, you're having to show us the world you're building. You don't have to go into Purple Prose territory, but it would help readers to become more ingrained if their other senses are engaged. So I'd suggest involving textures, smells, lighting, weather (humidity, dryness etc), and so on. This will give you a tangible feel. You don't have to stop the narrative to provide this info, but adding in bits here and there that give your audience the 'feel' of your scene can really bolster your readers all around experience.
One thing I also noticed right from the off, is that you've run into the 'Passive Voice' problem. Passive Voice is essentially telling instead of showing. You can end up in a situation where your narrative feels rushed and passed over due to the use of adverbs (-ly words) and instances of 'was', 'while', 'but' and, 'because'. The best thing you can do to fix some of these issues is use -ed words and minimize usage of fluff words. I'll use an example from your own text to illustrate my point:
Original: He quickly turned around and made his way back to room thirteen where he enjoyed his aunt's surprisingly delicious packed lunch in peace and quiet. Kaito made sure to stuff as much food as he could in his mouth because he knew once the bell chimed again he would have to make his way to the next classroom, which for all he knew, could be on the other side of this giant glass enclosure.
Edited: He turned and made his way back to room thirteen. He enjoyed the steamed vegetables and rice his aunt packed for him in peace and quiet, surprised at how delicious it all was. Kaito stuffed his face in record time; once the bell chimed again he'd have to sprint to the next classroom, which for all he knew, could be on the other side of campus.
The edited paragraph states the same as the first, but the word count has been reduced and only the necessary words are included. Removing fluff words tightens the narrative and enhances your reading flow. Now, these are things that everybody does once they get into their major editing phases, so don't worry! You'll get to it. Also, like I said, beware usages of -ly. These words can take your action out of the moment and turn it into a story told from a distance instead of from the character's perspective. You don't want to lose the direct line between your protagonist and your audience.
Another thing that immediately brought me out of the story was this bit right here:
"Guess I'm late for class... It's my first day at this school... It shouldn't be a problem."
This is a cliche and it immediately bumped me from your story. I cannot tell you how many books, cartoons, anime, manga, slice-of-life genre works start with the main character being late on their first day in a new school. It's almost synonymous with starting the story waking up from a bad dream, or a character looking in a mirror to describe themselves to the audience. Because of its overuse people immediately make bad associations to the trope (despite how good your story might be). This is something to be aware of when you go into your editing phase.
I will say I did like the very Midsummer Night's Dream moment with Miyu and Kaito on either side of the wall. I thought that was a funny scene and it rounded out their characterizations and those of their guardians. Kaito's aunt is more relaxed and casual and Miyu's father has a broken heart; how they interact with their kids in these little moments is a nice touch.
Unfortunately the aforementioned scene then leads into another area where things fall off for me: the 'bully' character, Ace. He feels like a caricature instead of a character. From the 'instant bully status' to the puffed up 'better watch your back' speech, the interest I'd been building off of the interactions of Kaito and his family, were derailed by this scene. Since we haven't really seen Kaito do anything to rub him the wrong way, it just seems cartoonish that a random bully would say 'hey new kid, watch your back!' without provocation. If there was something about Kaito, a rumor or something he'd done inadvertently (or who knows, Kaito has an attitude, maybe something he did on purpose) before this point, then it would feel more like a solid scene. As it stands, it just feels out of nowhere and very stock. When you do your editing phase, you might want to include an inciting incident before this, so that when this scene comes into play, Ace has a reason to start harassing Kaito, thereby adding some tension to the scene.
Another thing that I've noticed (and this is not just with your novel. This is a thing many novels that involve going to school have a problem with) is the clip at which your school days are over. I don't feel like Kaito is in school, because every day is the same thing: don't be late, find Touma, have a conversation/one event, go home, repeat. Granted, sitting through class IS boring, but outside of Kaito's friends and the fact that he's afraid of being late, I don't really feel like his school life where all of his friends are, has meaning. It all feels like it's being used as quick preamble to push plot points. (And to get him to the music club as fast as possible). Often times, we forget that our environments are sometimes characters too.
An example of this is in The Melancholy of Haruhi Suzumiya. The club room where they held all their meetings, scheming and activities (or prep for activities) took on a life of its own. (Now, this anime and light novel weren't my favorite things in the world, however, I did feel that the club room was very much a character and how each person used it both with others or alone, filled the space with its identity.) Sometimes a character would want to be alone, so they'd get to the room early and spend time with their thoughts, then someone would walk in and the atmosphere would change. Or, Haruhi would be doing something crazy and people would walk into a typhoon of ruckus. Either way, you'd have a feeling about the room you were going to enter.
To take this idea to the larger scale of encompassing an entire school: Full Metal Panic? Fumoffu involved classes, characters, principals, school and military officials. The school was the center of the action as the main character had to try and figure out what it meant to be a normal person (rather than a trained military captain who had no childhood) and where he figured that out was with the normal people he interacted with and the outrageous situations he put them in, all on school grounds. The school itself became a character, as you know when going in that you're going to spend the day with a paranoid ex-military captain searching his locker for booby-traps (when, in actuality, he got a valentine). The school itself felt like it involved the audience and so, when I think back to Fumoffu, the school is the first place I think of.
And yes, I do realize I used anime references but, your work reads like a light novel and has very anime-like elements in it, so I figured these references could be good ones. Examples of environments acting as characters in books can be found in Harry Potter (because Hogwards very much was a character), The Lion The Witch and The Wardrobe, and Miss Perigrin's Home for Peculiar Children. That's just a hand full but, you get the idea. The environment needs to play a role so your setting feels tangible to your readers.
As such, maybe seeing instances of Kaito slipping notes back and forth in one of his classes, or we see him interact with Touma or Himari in different classes early on so we feel like we're in his life with him. These are just ideas to consider when you do your major editing. How you want your audience to interact with your atmosphere and so on. Like I said, these are things that happen to EVERYBODY on their first few drafts so, you're by no means outside the norm here. It's important to get your ideas out and on the page so you can come back and refine later. As such, I've got some tools to help you out in that department! Alrighty the first is this guy: Editminion! This is a tool that identifies instances of adverbs, passive voice, weak words, cliches, homonyms and so on. It's a great little editing buddy that you can use to catch some of the small stuff that's easy to lose track of when you do your big edits.
Here's a quick overview of scene elements that can help you tighten up your narrative as you edit. Here's some examples of Active and Passive Voice, to help you identify them when editing. Overall I actually think you've got a sweet story here, the journey back to humanity for two people who have suffered and who have to learn to love others and themselves again. I think you'll carry this story far, all the editing will do is make what's already awesome shine.
Aaaaaaaaaand if you've survived until the end of this thing, huzzah! You lived! I hope this feedback helps you and I wish you the best of luck as you go forward. Also, fair is fair, I'll post the link to mine as well. There's quite a lot of material in this unedited tilt-o-whirl so, don't feel obligated to read through the whole thing lol, I know you're probably busy writing your stuff too. Thanks in advance and have a good day.