Lyre

They don't have to be a blank slate. I'm sure everyone is tired of the generic "white boy" MC in a furry game who has very quippy dialogue. I understand what you mean, but the type of self-insert character you are going for is usually new to the world or situation they are in. They are discovering it with us or are directly meant to represent the reader/viewer in how they'd think or try to navigate the story they are in. Examples are Johnny Cage from Mortal Combat and Randy Meeks from the original Scream movie. Those characters may not be like the reader, but they still think as we would. An average human with no connections or powers is thrown into a world of magic where the faith of everything they once knew is placed on their shoulders and a bunch of people they don't even know, but hey, now you've got freaking superpowers! Or, a horror movie fan was thrown into a horror movie situation saying everything we are shouting at the screen to the point of even calling out the killer way before their reveal. They can exist, but they are relatable and react to the new situations they are thrown into as the audience or a fan would. I don't feel that with the "player character"  of this game. Yes, all 3 have their own lives before the story we are presented, but your character acts just as their own person. And sure, that could be similar to Randy Meeks, but in his story, he says things fans of horror movies would say cause he's the surrogate. While your character is brilliant and well-versed in the world's rules like he is, we as an audience are not familiar with those rules like how we would be with the horror movie genre in Scream. Almost nothing needs explaining to them, and even when introduced to something you think they'd be unfamiliar with, they know more about it than the reader does. They don't do or react as a fan of these media types would but maybe once, and they are very familiar with their role in the world. Spoilers, when first introduced to what is essentially magic towards the latter half of the current story. They don't act as a vehicle for the audience to it. The character even always knows more than most think they would and is called out on how clever they are multiple times. Like, if they were unfamiliar with how the political sphere of being a foreign dignitary worked and were in the library constantly studying to pass off a feeling of competence or something, or was winging it and having the cast misinterpret their improv as genius by getting something very insightful from it that'd work. Though that wouldn't necessarily fit with the mood at first, with how drastically the tone shifts during the introduction of deities, it wouldn't be a stretch. 

The description being overhauled would undoubtedly be a welcome change. As it stands, it feels like it's advertising a different thing, and that cheapened the experience of what I was reading. The entire time I was waiting to see if I'd have any say in how to shape future events. I wondered if I could spend more time with the prince to see the side of him that other characters claim exists. I wondered if I could talk to certain characters to get a better feel for how the world looks through the eyes of someone who sees it as a more hostile environment. Instead, I wasn't given any of that. I was given a rather intriguing story I never once felt like I had entered into. I will not stop complimenting the story. It is delivered very well and certainly got me to read and re-read it, but I never felt any sense of other characters being smarter than the protag. Most seem to trust them and are surprisingly open. After playing this novel twice, the entire synopsis feels like it's only about one person, and you don't interact with them enough to even feel like they are trying to deceive you. It just feels like they never give you the entire story because they don't fully trust you. The romance isn't even unlikely. They are the character you spend the most time with, and never once does the character even question themselves on how they could have feelings for them. The lore even plays it off as if it's natural where they come from, and only in Lyre is it seemingly unnatural. It's self-evident they were meant to be the main romance from the get-go, which is partly why I was hoping to see if there were choices to branch out and get to know other characters. Because, again, the synopsis makes it feel like you can do that.
Honestly, if the synopsis is left as written, literally any other character being a romance option would make it feel more unlikely of a romance than what we end up getting. Imagine the scandal of two foreign dignitaries both befalling tragic events before their trips falling for each other while never feeling like they can ever fully trust one another. Indeed, if word through the court spread that they seemed relatively close, people would feel like their respective countries were trying to pull something shady against Lyre by controlling the crown.
Or imagine the story of the king's advisor who was smitten with the man he worked for, and somehow the king had feelings for someone beneath him whom he knew he couldn't ever be with due to how weak it'd make the crown seem. And to be later framed for their secret lovers' murder. The romance would be unexpected and go to a place you don't see visual novels ever go. Usually, they end when either of the romance options dies after all. Cause that's the fail state, that is the bad ending. But getting justice for the man you should never have loved? That'd be an exciting end goal.
Even if the romance were the prince, it would be interesting and unexpected with how he acts (though he'd likely have to be two years older because if I got the context clues right, he's 16. Even though adulthood in fantasy settings is usually more flexible, it wouldn't work with how most modern societies see things, bar places like Japan, Italy, Germany, Portugal, and some U.S. States). How would he feel if the person he had feelings for was the prime suspect in his father's murder? One of the people he slowly began to feel vulnerable around might've just been using him from the get-go to advance their political agenda in his eyes. That'd be an intriguing story.

I apologize. I lost myself. What I mean is I would have never thought that these would be possibilities if the synopsis were not written like it currently is (as of 1/11/2023).