bpy.types.BlendDataWindowManagers doesn’t support bpy.props properties, but bpy.types.WindowManager does. And it behaves like a global object, 'cause there is just one window manager (bpy.context.window_manager).
You should use the property option options={‘SKIP_SAVE’} on bpy.types.WindowManager if you need temporary (as in: not saved to .blend) properties across scenes.
If you don’t plan to add such a temp property to a panel, then use a class and class variables to store things globally (any python types), e.g.: