Do not repaint the interactive footer after Ctrl-D shutdown #32

Problem

Ctrl-D at an empty interactive prompt exits with code 0, but leaves the live composer box and ? for shortcuts hint on screen. Reproduced on main 9fb0d50 (0.3.3) and PR #29's original head ccf79b4; this is not introduced by #29.

Reproduction

1. Start the built CLI interactively in an 80×24 terminal and leave the draft empty.
2. Press Ctrl-D.
3. Wait for process exit and drain all remaining PTY output.

Actual: exit code 0, but the input box and shortcut hint remain as if they were still interactive. Expected: terminal cleanup completes without repainting the live prompt, leaving the cursor in a sensible position for the next shell prompt while preserving useful transcript output.

Verified with xterm.js 6.0.0 and a real macOS PTY. The bridge explicitly drained final output after process exit, so the observation is not based on dropping final cleanup bytes. Native Terminal.app shell handoff has not yet been checked.

Likely starting point

Inspect packages/cli/src/chat.ts: onKey() calls onControl() and then unconditionally refreshes; Ctrl-D can reach quit() → finish() during that control call. Check whether refresh runs after Screen.finish() has cleared/restored the terminal. Verify the lifecycle before choosing a fix.

Acceptance criteria

• Empty-prompt Ctrl-D exits 0 without redrawing the live composer/hint after cleanup.
• Normal terminal modes and cursor visibility are restored; settled transcript is retained.
• Tests cover post-finish output ordering and double Ctrl-C exit, without changing Ctrl-D delete-forward in a nonempty draft or Ctrl-C interruption during an active run.
• A visible PTY-backed terminal test drains final output and confirms a clean handoff to the next prompt.

Keep the change limited to shutdown/input lifecycle. Do not broaden it into active-tool process cancellation (#16/#17).