It's not you. Windows is designed to operate this way.
Your Book panel is a floating panel describing a separate file than your InDesign document. Since you have your InDesign application window set for full screen, by design the Windows operating system sets it to be displayed to the exception of any other applications on your screen.
While your Book panel isn't a separate application per se, it is considered a different document open within InDesign by Windows and will be put behind your full-screen InDesign application window for your document.
You can fix this by removing the full-screen view and then adjusting the size of the application window to take up your full screen. The effect will be the same, but the complication you're dealing with should no longer be an issue.Laubender's answer here is also worth remembering: like any other InDesign file open in the application, your book file will be listed at the bottom of the Window pull-down menu. So if it's open, your book file is only a couple of clicks away.
Hope this helps,
Randy