Shell command completion never detected when running inside tmux (output appears, but command reported "still running" forever)

### Describe the bug

When Copilot CLI runs **inside a tmux session**, shell tool commands execute and their **output appears correctly**, but the CLI **never detects command completion**. Even a trivial `echo hello` prints `hello` and then hangs indefinitely as "still running"; it must be manually stopped. Running the CLI **outside tmux**, the identical command completes immediately (`exit code 0`).

This is independent of tmux version and config. See matrix below.

### What this is NOT
Not the unfocused-pane keystroke bug (#4213): output is delivered fine and this is not about input/enter. This is specifically **completion/exit detection** of shell tool commands.

### Reproduction matrix
| Condition | Result |
|---|---|
| Inside tmux 2.7 | hangs -> "still running" forever |
| Inside tmux 3.3a (`escape-time 0`, `allow-passthrough on`) | hangs |
| Outside tmux | `echo hello` -> completes, exit 0 |

### Affected version

1.0.74-1 (also seen on prior versions starting from 1.0.70). Version 1.0.69 is unaffected

### Steps to reproduce the behavior

1. Start Copilot CLI **inside a tmux pane**.
2. Have the agent run a shell command, e.g. `echo hello`.
3. Output `hello` appears, but the command is reported "still running" indefinitely; only `stop` clears it.
4. Exit tmux, repeat the same command. It completes normally with exit code 0.

### Expected behavior

Shell command completion/exit should be detected the same inside and outside tmux.

### Additional context

### Environment
- Copilot CLI: **1.0.74-1** (also seen on prior version)
- OS: Linux
- Shell: /bin/bash, `TERM=xterm-256color`
- tmux: reproduced on **2.7** and **3.3a**

まず、`echo hello` を使って tmux の内外で問題を再現し、シェルコマンドの完了検出と終了ステータスを比較します。CLI によるシェルコマンドの完了検出を追跡し、tmux で異なる結果になる理由を特定します。両方の環境でコマンドが完了と終了コード 0 を報告すれば完了です。

索引モデルが issue の本文から書いたものです。