The cylinder's far edges fit into her sensory range, at least. It seems to contain multiple variously massive spiral staircases, many of them containing some manner of shelving and frequent landings. A few are wide, gentle ramps, rather than stairs. The larger staircases in main area of the cylinder are well-trafficked, but as she approaches she hears the shape of a few scattered small staircases tucked away into the stacks, where she'll be able to avoid people.
There's many, many levels of the library both below and above. Above, things seem to be mostly convenient and regular and very well behaved, and the library's increasingly crowded as the levels ascend.
Below - starting about a mile down - things get weird.
Shelves that move, ever so slightly, when she's not actively paying attention to them. A lake with no apparent bottom despite having another floor right under it, and the ceiling between them not being unusually thick. An area of humming crystals. Far, far fewer people, especially farther down.
And, about a mile and a half down, and a mile from the cylinder itself, there's a group of four children, apparently about age ten. One of them's sniffling. Two of them are arguing about taking the wrong turn a bit back. One's dragging her feet, shoulders hunched.
(Farther, near the very, very bottom of her range, there's a whisper like thousands of pages rustling.)
The cylinder continues up about two miles, though a few stair cases go past that and there's library in her entire range, and down past where she can hear.