Show timestamps on conversation messages

Feature Request

Add per-message timestamps to the Claude Code terminal UI.

Problem

When working across multiple terminal windows or long sessions, there's no way to tell when a message was sent or when a response was generated. This makes it hard to correlate activity across windows, gauge response times, or review session history meaningfully.

Proposed Solution

Display a timestamp on each message — either inline next to the user/assistant label, or as a subtle gutter annotation. Options worth considering:

• Relative time (e.g. 2m ago) while the session is active, switching to absolute on hover or after a threshold
• Absolute time (e.g. 11:42:07) as a dim annotation at the start of each turn
• Session start timestamp in the header as a minimum viable version

Context

Particularly useful when:

• Running multiple Claude Code windows in parallel
• Reviewing what happened during a long autonomous task
• Correlating Claude activity with external events (deploys, CI runs, etc.)

Would be a low-footprint addition — a dim timestamp on each turn would suffice.