[i18n] Add Korean localization for built-in UI labels in interactive prompts

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Title:
[i18n] Add Korean localization for built-in UI labels in interactive prompts

Body:

Summary

Several UI labels in the interactive AskUserQuestion prompt are hardcoded in English,
making the experience inconsistent for Korean-speaking users.

Affected elements

• Submit button
• Other (free-text input option)
• Chat about this
• Bottom keyboard hint text (e.g., ↑↓ to move · enter to select · ? for help)

Expected behavior

Support Korean (ko) as a display language, either by:

1. Following the system/OS locale setting (e.g., LANG=ko_KR), or
2. Allowing language configuration via Claude Code settings (e.g., settings.json)

Environment

• OS: Windows 10
• Terminal: Windows Terminal
• Locale: Korean (ko-KR)
• Claude Code version: latest

Additional context

Claude itself responds fully in Korean when prompted, and the question/label/description
fields in AskUserQuestion support Korean text without issue.
However, the framework-level UI strings (Submit, Other, Chat about this, keyboard hints)
remain hardcoded in English, creating a jarring mixed-language experience for Korean users.

Adding Korean (ko-KR) locale support would significantly improve usability for one of
Claude Code's growing user bases.

Proposed Solution

Proposed Solution

1. Locale detection

Automatically detect the system locale (e.g., LANG, LC_ALL, LANGUAGE
environment variables) and load the matching UI strings.

1. Settings-based override

Allow manual language configuration in settings.json:
```json
{
"locale": "ko-KR"
}

1. Fallback behavior

If no locale is set or the locale is unsupported, fall back to English (default).

1. Suggested Korean translations

| English | Korean |
|-----------------|------------------|
| Submit | 제출 |
| Other | 직접 입력 |
| Chat about this | 이 항목으로 대화 |
| ↑↓ to move | ↑↓ 이동 |
| enter to select | enter 선택 |
| ? for help | ? 도움말 |

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_