By default, the node library is docked within each open composition window. You can undock the node library by dragging or double-clicking its title bar. While undocked, only a single node library will be displayed no matter how many composition windows are open. You can re-dock the node library by double-clicking its title bar.
The symbols that represent macOS keys are listed in the introduction to Keyboard Shortcuts.
You can hide the node library by clicking the circle within its title bar, or by pressing ⎋ once (if the search bar is empty) or twice (first to clear the search bar, then to close the node library). Once hidden, you can re-display it by selecting or using ⌘↵. The same command or shortcut, ⌘↵, will put your cursor in the node library’s search box.
Whether you have left your library docked or undocked, visible or hidden, your preference will be remembered the next time you launch Vuo.