Feature request: show per-message timestamps in the chat UI

Summary

The VSCode Claude Code chat UI (both sidebar panel and editor tab view) currently shows no timestamps on individual messages. There is no way to tell when a message was sent or when a response was received.

Desired behavior

Show a timestamp on each message bubble — similar to standard chat applications (Teams, Slack). Suggested format: full timestamp on hover, short form inline (e.g. Jun 15, 2026 09:05).

Why this matters

• Session review: When revisiting a long session, it is impossible to tell how long a particular exchange took, or when during the day a decision was made.
• Cross-referencing: Users working across multiple tools (Jira, Teams, Outlook) often need to correlate "what was Claude doing at 10:15" with other system activity.
• Session identification: No date/time context when multiple sessions are open — timestamps in the conversation thread would help identify which session is which.

Notes

• The underlying .jsonl session files already record timestamps on every entry — the data exists, it just is not surfaced in the UI.
• Applies to both the VSCode extension panel and editor tab view.
• Terminal (claude CLI) is out of scope.