VS Code extension: clicking notification should focus the correct Claude Code terminal

Problem

When running multiple Claude Code sessions across different VS Code windows and terminal tabs (e.g., 3 workspaces with multiple sessions each), there's no way to jump directly to the session that needs attention.

Currently, the Notification hook can trigger a macOS notification via terminal-notifier or osascript, but clicking it can only bring VS Code to the foreground — it cannot focus the specific terminal tab that triggered the notification.

Proposed Solution

The VS Code extension should provide built-in notifications (using the VS Code notification API) that, when clicked, focus the correct terminal tab/panel containing the Claude Code session that triggered it.

This would be especially useful for:

• Multiple concurrent sessions in different terminal tabs within the same VS Code window
• Multiple VS Code windows open for different repos
• Long-running tasks where you switch away and need to return to the right session

Current Workaround

Using terminal-notifier with -activate com.microsoft.VSCode brings VS Code to front, but you still have to manually find the right terminal tab. Per-repo icons help identify which project needs attention, but not which tab to click.

Context

Related issues:

• #6091 — Support IDE-level notifications for claude-code plugins
• #11156 — Notification hook does not fire in VSCode extension
• #22702 — Allow suppressing background task notifications