Move some #includes around to match the Contributing guidelines.

ControllerInterface: Adjust sort priorities to ensure default keyboard-mouse device is first.

Enable emulator hotkeys and controller input (when that option is
enabled) when a TAS Input window has focus, as if it was the render
window instead.  This allows TASers to use frame advance and the like
without having to switch the focused window or disabling Hotkeys Require
Window Focus which also picks up keypresses while other apps are active.

Cursor updates are disabled when the TAS Input window has focus, as
otherwise the Wii IR widget (and anything else controlled by the mouse)
becomes unusable. The cursor continues to work normally when the render
window has focus.

This was broken by a9a9fdd9e9. Because Init didn't run, the Android
input backend would crash whenever it tried to call into JVM code.