The hotkeys you are asking about have no meaning in the menu. How would you focus the Omnibar when the menu has none? How would open the DevTools/JS Console for the menu? How would Ctrl+U makes sense to view the source code of the Wrench menu? Those keys only apply to browser windows/tabs. When you open the menu, you switch from the context of tab, to the context of the menu.
Close the Wrench menu and the hotkeys will work for the currently active tab.