Feature request: copy button for individual chat messages

Problem

Codex and other AI chat interfaces in VS Code have a dedicated copy button that appears on hover for each message. Claude Code extension lacks this — the only way to copy a full response is manual text selection, which is tedious especially for long outputs.

Code blocks already have a copy icon. The same pattern should apply to prose responses.

Expected behavior

A copy icon appears on hover at the top-right corner of each assistant message, copying the full message content to clipboard.

Why it matters

When using Claude Code alongside other tools (e.g., reviewing output in a second AI), copying responses quickly is a core part of the workflow. The current friction breaks focus.

Environment

• Claude Code VS Code extension
• Linux (Devin environment)