ActivityManager.qml doesn't have input method issue because the initial
focus is inside the text field. So here we try to apply the same logic.
Always force focus into the text field first, and handle the rest of key
event accordingly. So we don't need to use event.text to append or do
anything special, because event.text is not a input method compatible
way to handle input.

Manually test arrow key navigation. Also test input method typing is enabled
when menu is opened.