Punchline in the first sequence is lacking; a confused cough isn't funny. I think a lost question from somepony struggling to keep up would be better.
They also served another purpose; the solid oak furnishings were enchanted to automatically block the doors in the event of a magical accident. This was for the safety of those within and without; polymorphed ponies could be... unpredictable, to put it mildly.
"Polymorphed ponies"? Polymorphed into what?
Celestia’s School for Gifted Unicorns, despite its prestigious reputation, was absolutely the wrong place to hold any sort of formal affair. Sure, there were grand lounges for the professors to while away their idle hours, waxing on about their latest research, but this was no place for student’s hooves to scuff the carpet.
Huh what? The sentences don't follow
Under any normal circumstances, the two of them would’ve rather spend time with floor paneling than each other. Then again, these were far from normal circumstances.
The full stop, "Then again" transition is jarring. Think about it and verbalise it and come up with a more natural phrasing.
Summer’s story was quite different. Twilight had been forced to attend a teacher’s luncheon with other promising students. Which meant the teachers got to fawn over them
Same problem here.
and ended up right at Twilight’s side, chatting it up like they’d known each other for years. An interesting pony, to say the least.
And here
ice rang with unquestionable authority. Twilight fell silent and nearly cowered under her desk. “This is for your own safety. I will not have you performing such dangerous spells before-
Missing end quotation
That was the worst part, that they should have the gall to rob him of
Dougnut Joe’s Twin-Topping Tuesdays.
Typo
In the waning hours of Celestia’s sun,the testing room took a far more gloomy mood in her lamplight.
Inconsistent "her"/referent
Overall;
Nothing stood out to me as wrong or inconsistent (with the disclaimer that I'm tired and not fully engaged with the world). I'm not hooked yet; I haven't encountered that moment that commits me completely to the story, but that doesn't mean it won't come. I don't think it should be delayed too much longer; the intro is solid, but now it's time to drop us into the real body of the story. Keep at it!