New option beside the physical-keyboard mode: Keep the keyboard on
screen.

The on-screen keyboard normally hides while a hardware or Bluetooth
keyboard is attached. With this on it stays up, which is what that mode
wants - its point is to have keys on screen for an app that believes
hardware is typing at it.

It cannot conjure the keyboard into an app that never asks for input:
an IME runs when an app starts input, and where there is no editor there
is nothing to show it over.
