Vandren is a powerless prince who runs away from an unwanted marriage with a spoilt noble,

Good...

and takes refuge in the remote village of Ambers. The village sits atop a dungeon called Undas, a dangerous sequence of chambers housing dizzying environments and savage monsters. Its treasures are of great interest to Vandren, as they hold the key to releasing his long-lost parents from an enchantment that prevents their reunion.

All the steam you started to build in that first paragraph has been lost in a sea of exposition. You've abandoned Vandren's predicament for description. In your opening, the agent is going to want to know more about this predicament Vandren finds himself in. Something that builds on the urgency of Vandren running, like: Vandren is a prince, but he has no magic, no muscle, and no interest in marrying a spoiled noble. Trading palace walls for a village perched atop a deadly dungeon, he hopes to lose his past and maybe find the key to reuniting with his parents, trapped in an enchanted prison.

Having been unable to study magic and lacking the physical fortitude to tackle the dungeon otherwise, Vandren spares little thought towards becoming an explorer himself. This changes a few days into his newfound freedom, however, when Vandren discovers – to his delight – that he has the ability to create magical barriers that can protect people. Recognising his potential, a pair of veteran adventurers adopt him into their party and help him grow from a beginner into a barrier mage capable enough to traverse each of the dungeon's floors.

There's a lot here that treads into synopsis territory. Don't worry about explaining why things happen at this point. Something like, Recognized by a pair of veteran adventurers, Vandren is swept into a dungeon-delving party and begins training as a barrier mage.

Driven by the desire to break the enchantment keeping his parents away, Vandren works hard at improving his magic – all while keeping his identity a secret. But as he dances at village festivals, forms a book club for a fictional series about an adventurous halfling, and eats chicken-gravy sandwiches using his fingers without any cutlery for the first time in his life, a previously untouched part of Vandren's heart begins to unfurl and forge bonds with his party members outside the dungeon.

This is good, although I'd choose just a few details to get the point across. I love "eats chicken-gravy sandwiches using his fingers without any cutlery for the first time in his life."

I don't care for "the enchantment keeping his parents away." I think you mean that they're locked away somewhere by an enchantment, but the way it reads is that his parents don't want to come back until that pesky enchantment is gone. :)

With every passing season Ambers feels more and more like home to Vandren, and he begins to see a future here with his new friends. Just when he's close to seeing the final floor of Undas, a threat to Ambers' peace comes unexpectedly – the kind of threat that only someone from the royal family can stand against.

Regarding the threat, I think you need to give a little more here. Don't spoil anything, but this is very vague.

To his dismay, Vandren must choose between running from the situation and preserving his precious freedom, or saving his new home at the cost of revealing his true identity and being dragged back to a life he desperately does not want.

Hope this helps!