I think that by "global" they mean that it's on top of the screen, rather than on top of the main window of the app to which it belongs. It's actually hella confusing for new users when they get to running apps in parallel, and switching between them. This is exacerbated by not having well-functioning maximize on windows, so a typical macOS desktop is cluttered with windows from several different apps - but the top menu is relevant to only one of them.

Shortcuts for menu items are normally shown in menus on Windows and Linux, right-aligned next to the label. For Windows, it's part of the platform UI design guidelines, and if you're using standard APIs to define your UI, any item with a shortcut assigned will render appropriately.