Its interesting stuff.
I've just been reading about some of the scrolls they have found and how so many have been so destroyed in the pursuit of trying to read them as they are so fragile and old. Its such a double edged sword, all that exciting information and not being able to easily get to it. (The scrolls i was reading about were from Herculaneum but from the sounds of things from a large upper class residence rather than a library.)
Same building. Given the size of the collection of writing, I think "library" is appropriate. I suppose it's technically a study, but I think of it as a private library.
There's even more to it than the scrolls you were reading about, though. Only part of the residence has been uncovered. It appears that there's a lot of it still buried. It was common in those days for the lower floors to be the higher status floors, so it has been suggested that the library discovered so far, the source of the scrolls you were reading about, is a secondary library and
not the main private library of the residence.
I understand the position of the Italian government. The parts still buried are being preserved far more effectively than could be done if they were excavated. Preserving the parts already excavated is a huge job that's been done extremely badly in the past and is a major challenge even today and a major expense. I think they're right to refuse permission for further excavation, that doing so is the course of least harm. There's also the issue of there being a modern town in the same location, which would be a problem for any further excavation. But...what's in the buried parts? If there is a higher status library further down, with rarer works, it would almost certainly contain writing lost since antiquity. There's a lot of writing that we know has been lost (because references to it remain) and no doubt there's a lot more that has been lost entirely without even a reference to it remaining. But I think they're right to refuse permission at least until the scrolls are readable. There has been experiments with non-invasive scanning techniques that have had some success on a small scale. More information about the scrolls has been discovered without damaging them and the results indicate that it might be possible to (very slowly and very expensively) read the scrolls without damaging them. But even after that...how do you preserve a huge ancient building once it's been exposed to the elements and plants and animals? Would it still be better to leave it buried until perhaps in the future better preservation is possible? A difficult decision.