Support Kiro CLI completions in Codex and Claude Code embedded terminals

## Request

Please support Kiro CLI Completions in embedded terminals used by coding-agent applications, including Codex and Claude Code.

The autocomplete dropdown and inline suggestions should be available when shell integration is installed and Kiro CLI is running.

## Observed in Codex

In the Codex desktop app embedded terminal, `kiro-cli doctor` reports:

```text
Terminal support: Unsupported terminal
__CFBundleIdentifier:
```

As a result, Kiro CLI Completions cannot be used there.

### Steps

1. Install Kiro CLI and enable shell integration in zsh.
2. Open a terminal tab inside the Codex desktop app.
3. Run `kiro-cli doctor`.
4. Observe the unsupported-terminal result above.
5. Type a supported command such as `git`; the Kiro completion dropdown does not appear.

The same Kiro CLI installation reports healthy configuration in macOS Terminal.

## Claude Code

Claude Code embedded-terminal support is requested as a related target. I have not reproduced it in this report.

Start with the `kiro-cli doctor` entry point and the shell-integration path described in the report. Reproduce the unsupported-terminal result in the Codex embedded terminal, then check Claude Code as a related target. Done means the completion dropdown and inline suggestions work in both embedded terminals when shell integration is installed and Kiro CLI is running.

Written by the indexing model from the issue text.