[FEATURE] Reuse existing Chrome tab group instead of creating new ones

Problem

When using Claude in Chrome, a new tab group is created for each task, even when a completed tab group already exists. This leads to accumulating tab groups.

Current Behavior

1. Start a task → Creates "⏳Claude" tab group
2. Task completes → Tab group becomes "✅Claude"
3. Start a new task → Creates a new "⏳Claude" tab group instead of reusing the existing one

Tab groups accumulate over time.

Expected Behavior

When starting a new task, if an existing Claude tab group is available (especially a completed ✅ one), reuse it instead of creating a new one.

Related Issues

• #15436 addresses tab group accumulation via cleanup after sessions end
• This issue proposes preventing accumulation in the first place by reusing existing groups

Environment

• macOS
• Claude Code + Claude for Chrome (Beta)