Spike: Gamepad Input Feasibility for Dead Reckoning

Goal: Confirm that Godot 4's input system can support controller navigation for a menu-driven terminal UI, and identify any rough edges before we commit to it.

Questions to answer:

1. Can InputEventJoypadButton / InputMap actions coexist cleanly with the existing keyboard bindings, or do they conflict?
2. Does Godot's built-in Control focus system (d-pad → ui_up/down/left/right) work well enough for navigating our terminal screens, or do we need custom focus logic?
3. How reliable is hot-plug detection (Input.joy_connection_changed)? Does it behave on Windows, Mac, and Linux without extra configuration?
4. Does Input.start_joy_vibration work on common controllers (Xbox, DualSense) without a plugin?
5. Can we detect "last input device used" reliably enough to swap keyboard vs. gamepad prompt glyphs at runtime?

Definition of done: A throwaway scene with two focusable buttons and a label. Plugging in a controller navigates between them, A confirms, B cancels, prompts update to show gamepad glyphs, and a short rumble fires on confirm. Hot-plugging during the scene doesn't crash or freeze.

Time-box: 2 hours.

Update: Done and pushed in 1.6. See release notes.