Perl/Tk cannot access the native menu bar on modern macOS (i.e. OS X), the main reason being that it still requires XQuartz, and anything run from XQuartz has no knowledge of nor access to the Mac menu bar. The documentation for Perl/Tk's Tk::Menu is quite old, and was likely adapted from whichever historical version of Tcl/Tk it's based on. So the Apple menu it's referring to is likely the one from classic Mac OS 9 and earlier, i.e. pre-Mac OS X.
To clarify, .menubar.apple refers to the "application menu", the one with the currently-focused program's name. The "Apple menu" (the one with the Apple logo) is off-limits to programs.
Tcl/Tk wrappers for Perl (Tkx, Tcl::Tk, and Tcl::pTk) should be able to use the Mac menu bar and its application menu on OS X, as long as Tk Aqua is used rather than Tk for X11. For this I would refer to the up-to-date Tcl/Tk documentation on "Special Menus in Menubars", as well as TkDocs' entry on Platform Menus which even has Tkx syntax examples.
As the co-maintainer of Tcl::pTk, I wish I could say I knew how to use the Mac application menu, but unfortunately I have not yet had any success…