Chrome extension: MCP tab group appears grey on Chrome startup instead of yellow

<img width="411" height="96" alt="Image" src="https://github.com/user-attachments/assets/1b47c8d6-fbef-4a20-aeba-dd438d8e76e7" />
<img width="496" height="91" alt="Image" src="https://github.com/user-attachments/assets/262b7c9e-18d7-48b9-84a2-30a06a792059" />

Bug Description

When Chrome is restarted, the MCP tab group loses its yellow color and "Claude (MCP)" title, appearing as a grey collapsed dot in the tab strip.

Clicking the grey dot or establishing a Claude Code MCP connection restores the correct yellow "Claude (MCP)" display.

Steps to Reproduce

1. Have Claude Code connected to Chrome via MCP (yellow "Claude (MCP)" tab group visible)
2. Quit Chrome completely
3. Reopen Chrome (session restore)
4. The MCP tab group appears as a grey collapsed dot — no title, no color

Expected vs Actual

Expected (normal): Yellow "Claude (MCP)" label in the tab strip
Actual (bug): Grey unnamed dot in the tab strip

_(screenshot will be attached in a comment below)_

Workaround

• Click the grey dot to expand it, or
• Start a Claude Code MCP session (calls tabs_context_mcp, which restores the group properties)

Environment

• Chrome 145.0.7632.46 (macOS)
• Claude Chrome extension v1.0.49
• macOS (Darwin 25.2.0)