Add timestamps to chat messages

Feature Request

Add visible timestamps to user and assistant messages in the Claude Code CLI conversation.

Problem

During long-running sessions (multi-hour automation tasks, overnight processes, etc.), there's no way to know when a particular message was sent. This makes it hard to:

• Correlate chat messages with log timestamps from background processes
• Know how long ago you asked something
• Review conversation history with temporal context

Proposed Solution

Display a timestamp (e.g., 14:32 or 2:32 PM) next to each message in the conversation. Could be:

• Always visible in a subtle/dimmed format
• Togglable via a setting or flag
• Shown on hover or via a keybinding

Context

Came up during a multi-day automation session where I needed to cross-reference when I asked Claude to do things with timestamps in process logs.