How to remove built-in shelf without damaging
Hard to tell how it's attached without taking it apart. It can't be just glue, so there must be something else. Could be dowels. Could be screws (in which case, the heads might be visible on the other side of the upright, where the piano book is sitting)

That shelf is a permanent part of the house, it wasn't built to be removable. It's going to be really difficult to remove, and there's no way to avoid leaving ugly scars behind. If I were you, I'd just leave it.

If you insist, then maybe you could use a flush-cut saw (and hope there aren't any screws or other metal in there).