Pre-emptive apologies: If I come off sounding like an asshole in this post I sincerely apologize because that isn't my intent.
I'm not sure you're remembering the game all that well because a lot of your points don't make a lot of sense considering the game is still fresh in my mind from a when I finished my trophy runs last week. I really hate getting into spoiler territory but here we go.
First, you're clearly wanting a JRPG that is more serious and focuses heavily on whatever the big bad is up to with little world building. I imagine a game like FF7 Remake is more up your alley in that case. The Trails series has always been about little interactions that ultimately have no major impact on the greater story as a whole and deal more with the characters themselves and pretending Cold Steel doesn't have plot just because a chunk of the game is about the interactions at Thors Academy is just silly.
Starting with Alisa's little outburst over landing on Rean at the start of the game, that plot is resolved by the time you reach chapter 1 with small throwbacks to it sprinkled through the story, mainly when one of the other students wants to pick on her during side conversations. The conflicts between Class VII's students are written in a way that emphasizes the differences in society in Erebonia because the game isn't just "Big bad wants to destroy the world" like most JRPGs are.
Fie and Laura's, and even Jusis and Machias's arguments are talked about fairly well during the school intermissions and while the former's arguments start as a random quip from the students on their way to a train its given plenty of explanation over the course of two chapters where you learn in Heimdallr that it is due to Laura believing Fie is refusing to put her all into combat and holding back as a member of a Jaeger corps considering her own upbringing as a daughter of one of the world's strongest swordsmen. Yes it could have been written a little better at the start but its an important part of character growth for the characters in this series.
All of the students get a decent amount of screen time and focused attention during the story but considering this is a series that's designed to resolve itself over the course of at least 4 games. I'm not going to spoil the ending for the sake of anyone reading this but Emma has a big buildup towards the end of CS1 and the plotline is left open due to events later in the series with certain characters that play a big role. While it would have been nice to see more in the main story about Emma there is a lot of background given through bonding events to the point where they almost spoil the finale of CS1. Again, the game is about characters and their relationships in a world with a major divide in classes. Many story threads are actually found in conversations that aren't related to bonding events and this is a staple of the Legend of Heroes series. In fact, Trails in the Sky foreshadows a major event in Crossbell through a random piece of NPC dialogue that has nothing to do with the main story or a side quest.
You seem heavily fixated on these fetch and monster hunt quests but its the main quest structure in every single entry of the LoH franchise. Just look at the Sky trilogy which has so much of these quests and a hundred times more moments of backtracking where they do nothing to further the plot, only to "increase your Bracer guild rank". At worst you have 3 quests during each field study day and all but a few end up leading right into a major plotline that advances the story. I'm not sure why the school festival is so offensive to you though...seems kind of silly when you literally do the exact same thing in Sky. The only difference is that instead of a quick festival at Jenis Academy where you're force volunteered to enter a play the festival at Thors is just more fleshed out and given a bit more life.
My time with the game was short because ultimately its not that long of a game. People exaggerate RPG game time a lot and the LoH saga is no stranger to being over-embellished by fans or exaggerated by detractors of the series. I used the turbo button to skip long screen pans and battle animations after I had seen them once before but I didn't skip anything outright. Cooking isn't a sidequest and much like the books all you do is talk to people to get recipes or buy a recipe book at certain points in the story.
You seem to be misremembering a lot of things with the game but the one big problem I have with Cold Steel as a series is Rean Schwarzer. He's an ultimately boring catch-all protagonist prone to anime bullshittery but that's probably the only real bad part of the series. It took me 65 hours of actual play to get the platinum trophy due to needing 2 playthroughs for bonding trophies. 35 hours of the platinum was me leaving the game running at the finale after all other trophies were obtained for the 100 hours trophy.
Play the Trails games for the world around the main plot, not the main plot itself. Falcom's greatest strength is that their games are almost always anime nonsense so if you don't want anime tropes like school festivals, slice of life things or dumb interactions like the whole Alisa falling on Rean bit being played out for a length of time then maybe the series just isn't for you.
