Hmmm the first thing I would do is break up the summary in more sentences, because at the moment it's one huge line
Original:
Reclusive young Era Vanaura and her friends Karo and Cawdigon live in a world within the mysterious Library, a infinite and sentient structure that has housed various worlds for billions of years, but are determined to earn enough money and supplies to leave their planet for good in order to find the fabled "Exit" - a mythical place said to grant the wishes of any who manage to find it.
This (well atleast to me) can feel a bit intimidating and scary for new readers. Let's see...
Rewritten summary (ok that was a pun):
Reclusive young Era Vanaura and her friends Karo and Cawdigon live in a world within the mysterious Library, a infinite and sentient structure that has housed various worlds for billions of years.
However, they are determined to earn enough money and supplies to leave their planet for good in order to find the fabled "Exit" - a mythical place said to grant the wishes of any who manage to find it.
It's not a big change, but it gives a little more breathing room to the potential new reader.
As for the actual summary itself, I'd say it is solid enough.
It introduces the main characters, the world they live in, a special goal they want to reach and the way they are going to achieve it! I think content wise it describes (almost) everything a reader needs to know.
The only thing I would maybe add is if there would be a antagonist that tries to stop them from reaching their goal. That would add a stake alongside the goal. But I don't know if you have one so that is your call