Every menu has a properly underlined Alt+key assignment (including About mini app) but most key assignment do not work -- some do. For example, Exit works with its Alt+key assignment but is erroneously labelled as Ctrl+key, which does not work. This is not just a problem in Kate but most KDE apps -- for example, check out Muon Package Manager.
Menus are a bit special: They show the shortcuts you can use _instead_ of opening the menu and selecting an entry there. The underlined accelerators in menus are special, too: They work _without_ the Alt key when the menu is open. While this is confusing and different from non-menu widgets, we cannot change it. You would have to talk to Qt developers if you have an idea how this can be improved. Use https://bugreports.qt.io/ or use a Qt developer forum first.