cmux: Korean IME composition broken (jamo separated) after Fn key press

Bug Description

Korean IME character composition is completely broken in cmux terminal. Instead of composing Hangul syllables (e.g., "한글"), each jamo (consonant/vowel) is entered separately (e.g., "ㅎㅏㄴㄱㅡㄹ"). This also affects other apps like KakaoTalk, indicating cmux may be interfering with the system-wide IME state.

Steps to Reproduce

1. Open cmux terminal on macOS
2. Switch to Korean input (2-Set Korean / 두벌식)
3. Press Fn key twice (or interact with cmux in a way that triggers input source change)
4. Try typing Korean — jamo are not composed into syllables
5. The issue persists across all apps (KakaoTalk, etc.) until system reboot

Expected Behavior

Korean characters should compose normally (ㅎ+ㅏ+ㄴ → 한)

Actual Behavior

Each jamo appears separately: ㅎㅏㄴㄱㅡㄹ instead of 한글

Environment

• OS: macOS 26.3.1 (Build 25D771280a)
• Claude Code: 2.1.81
• Input Method: com.apple.inputmethod.Korean (2-Set Korean)
• Keyboard Layout: ABC
• Fn Key Setting: "Emoji & Symbols" (Dictation is OFF)

Workaround

System reboot resolves the issue temporarily, but it recurs after interacting with cmux.

Notes

• The Fn key double-press may be triggering an input source switch that disrupts IME composition state
• The issue affects system-wide IME, not just cmux terminal
• Clicking outside cmux and back does not fix it
• Restarting cmux alone does not fix it — full system reboot required