When global menu is enabled in system settings, konsole will respect this config and shows a global menu. But after re-login, the konsole window will be opened with default menu setting(no global manu, just ordinary menu panel). Then you can close all those restored konsole windows, open a new one, the global menu will be back.
What theme are you using? All I see for Breeze is: "in application", "title bar", "Application Menu widget"
Breeze title bar
Yes I see what you mean - I think all that is behind the scenes - do all other KDE apps work as expected?
Did a simple test,Kate did not as well while dolphin did respect