The staircases do have a rotation of 60 degrees and not 90. It's exactly because of the reason you just explained, namely to ensure that every hexagon is reachable, especially the ones on the same floor that you are currently on. Right now you can go to a neighbouring hexagon that is not directly connected to the one you're in via a hallway by walking up a staircase, walking to the next hallway and then walking back down a staircase.
Here's a sketch of the library structure I made back when I was trying to figure out how I needed to design everything for it to work: