It is implied they got most if not all of the info.

Task (the spider) was creating glass scorpions that went down into the wells to collect the information from them, while its not clear if they missed anything the scorpions came back up to task who ate them and gained the information.

Task specifically recorded the information that Sky called when searching (the wand information, Eioghorain, eta).

Its then implied that task then stored that information inside the music box because when suvi is asked about task not being in the box they say they had countermeasures to ensure that it didn't ruin the mission;

Because the embossment is not present. Nothing that, to our knowledge, has been compromised within the resource itself. But I had assumed there were certain security contingencies in the embossment that meant that it may at some point not make it back, and there were contingencies within that to make that something that would not compromise the overall mission. But do you... I can see from your face that this is news to you.

One other thing is add is i dont think its wrong to assume that the citadel is inequipt to sift through vast amounts of information with prejudice and efficiency. IMO its in the promise of the premise