[FEATURE] Syntax highlighting in VS Code extension chat panel (re-opening closed requests)

Summary

The Claude Code VS Code extension renders fenced code blocks in the chat panel as plain monochrome text. No syntax highlighting is applied regardless of the language tag (typescript, python, diff, etc.) or the user's active VS Code theme.

Context

This has been reported before but both issues were closed by the stale bot without a maintainer decision:

• #54295 — Add syntax highlighting to fenced code blocks in the VS Code extension chat panel
• #21667 — Code blocks in Claude Code's chat interface only show a dark background without full syntax highlighting

Since code suggestions are the primary output of Claude Code, reading monochrome code is noticeably slower. Users already have grammars, language servers, and themes configured — the chat panel is the only place that ignores them.

Proposed implementation

VS Code exposes APIs for exactly this:

• TextMate grammar tokenization via vscode.languages — renders with the active theme, no extra dependency
• Shiki (same lib VS Code's markdown preview uses) — lightweight fallback

Expected behavior

Code blocks are tokenized by their language tag and styled with the active VS Code theme, matching the editor appearance.