This is actually a really cozy experience! I really love Godot Engine, so the things you're doing here are super awesome for me. The game itself plays really well, and there's only a few issues I could spot. I'll shoot you a bug report to your e-mail as well.
Music, art style and dialogue are definitely peak for me. Sound design-wise there's a few issues - I believe the blip sound rate for dialogues is a bit excessive, and causes individual blips to cut each other off, causing clipping. It's grating on the ears, so you could either make it so individual blips can never play over each other (wait for previous blip sound to finish before playing the next one), or make it so blip sounds only play once per every two letters (the way Ace Attorney handles it).
Additionally, I ran into a bug with the sliding table puzzle, where sometimes (somewhat rarely, but it managed to happen once per classroom) a single keypress to move in a direction would register twice, causing the table to overshoot - I have a couple of guesses why this happens. It could be related to the frame skip option (I have it on V-Sync), or it could be the _process(delta) function not using the delta. Alternatively, I could guess you are using _physics_process(delta) instead, which you shouldn't do unless physics are actually involved. Ofc without seeing the code, I can only guess and grasp at the information that's available to me, but hope this little insight is helpful.
Oh and the art - I'm extremely impressed with it. The characters are expressive, and I really like the face and pose variety for each character. The pixel art is also suitable. I like what you did with the classrooms and how there's some light coming in from the south side, though weirdly enough, the middle classroom lights overlay the character, while other classroom lights disappear under the light2d emitting from the character. Is it a missing mask?
There's not many music tracks on display yet, but what I'm hearing right now does the job very well. My favorite track is definitely the "school at night" one, though it might be because I've listened to it the most to get really familiar with it due to gameplay.
Finally, the dialogue, and the amount of choices you let players handle, is staggering. The way how you can seamlessly be a nice person (making friends with the girls) or an asshole (using their strand of hair instead of your own) without any "morality indicator" outside of immediate consequence of your actions makes the game feel a lot more personal, even if those choices have no impact on the story or ending you obtain (maybe a yes/no option when you use scissors on a girl would be helpful to warn the player they can do this kind of thing, though). I would hope for there to be multiple possible routes depending on how much of a dick you want to be to people around you, I would be fine even if there's just one satisfying conclusion that makes sense regardless of the choices the player is allowed to make.
Sorry to prattle on about this game, I'm just really excited for the project and I want to see it grow into something amazing. You did an awesome job with the first impressions, now to knock it out of the ball park with the full release! Best of luck :)
EDIT: Oh yeah, any plans to release the source code for just the engine once it's in a spot you want it to be? It would be an amazing resource with what you have already!