So far (25 chapters in) Academy's Genius Swordsman a pretty typical Korean regression/academy story. It could very well be your first gateway into the genre, because it hits ALL the bases, and ticks ALL the boxes.
A protagonist filled with regret over a world he couldn't save? Check.
Returning to a younger body with all his tactical and practical knowledge intact? Check.
Befriending all potentially useful and influential people he knows of, and then some? Check.
Impressing and/or punishing comically villainous higher-ups and seniors who can't properly evaluate his potential? Check.
Getting lots of money from the start, the absolute best gear and also a magical mascot pet that trivialize most battle encounters? Check, check, check.
Not much actual world saving but wacky "magical school for rich kids" shenanigans while the clock is ticking? Yeah, you got that. Check.
Enemies fear him, guys want to be him, girls want to be with him. Actually, no, it doesn't feature much romantic content so far and there's a pretty obvious "best girl" presented early on, but there's truly no one who's indifferent when he's around.
While the manhwa is overall competent in terms of art, storytelling, and characters, I just can't really wrap my head around MC's power levels. You'll probably be asking this yourself, too: did he actually need to to back in time? Or rather, did he actually need to enter this academy that's literally in the title?
Like, why? What's there for him to learn even? Though you could say he's good at learning because he can copy and perfect ANY technique after only seeing it once.
He's already the most powerful, the most capable, and the most flashy swordsman of this generation, and on rare singular occasion he loses, it's because his weapon just can't withstand his awesomeness. I shit you not, the hugest obstacle so far is that there's no sword that can sustain and channel his immense power (which is not even fully developed I guess, because he's this good even without using mana/aura).
Are there more powerful individuals in the world at this point in time? Ehh, just one, I suppose? But I'm pretty sure if they have a rematch/show-off when he has a shiny new artifact-grade weapon, this score will be settled as well.
So, I don't know. It's okay. It's alright. It represents the genre well but doesn't really say anything new on the topic. Does it need to though — that's the question you'll need to answer yourself.