[Feature Request] Add timestamps to conversation messages in Claude Code UI

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

Summary

Claude Code's conversation UI does not show timestamps for individual messages.

Problem

In long technical sessions (e.g., iterative debugging, multiple builds,
test cycles), it is impossible to correlate a message with a specific
build or external event without timestamps. Tools like WhatsApp, Teams,
and VS Code terminals all show message times for this reason.

Use case

Example: during a build/test cycle, the developer sends a crash report.
Without timestamps it's unclear if the crash refers to build X compiled
at 15:47 or build Y compiled at 16:03.

Proposed Solution

Proposed solution

Show HH:mm or HH:mm:ss timestamp next to each message, similar to
standard chat tools.

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_