Feature request: inline message timestamps

Feature Request

Add optional inline timestamps to messages in Claude Code conversations.

Use Case

When running long-lived Claude Code sessions (especially via orchestration tools like agent-deck where sessions persist for days/weeks), it's very useful to know when messages were sent from both sides — user and assistant.

Currently the only time-related display is showTurnDuration which shows turn processing time, but not actual wall-clock timestamps.

Proposed Behavior

• Optional setting (e.g., showTimestamps: true in settings.json)
• Displays a timestamp (e.g., May 19 14:32) next to each user and assistant message
• Useful for:
• Long-running sessions that span hours/days
• Multi-session orchestration where you switch between sessions
• Debugging timing issues
• Reviewing conversation history

Alternatives Considered

• Hook-based logging to a side file (works but loses the inline benefit)
• showTurnDuration (shows duration, not wall-clock time)