In Delphi 7, the application window (on the taskbar) is also hidden when the main form is hidden.
As I said above, window button on a taskbar is always hidden when corresponding app's window is hidden. It is a functionality of Desktop Environment, not application.
And yes, it is quite unclear, why someone needs to
hide a window, but keep taskbar button visible. Looks more like a
minimize behavior.
More often they need an opposite action: hide button from taskbar (optionally move icon to the tray) but keep window visible.