[BUG] Cowork mode: GitHub connector shows Connected but exposes no tools to Claude

Description

The GitHub connector shows as Connected in Cowork Connectors settings, but Claude has zero GitHub-related tools available. The MCP registry search (search_mcp_registry) also returns no results for "github". The Gmail connector works perfectly in the same session.

Steps to reproduce

1. Connect the GitHub connector in Cowork settings (shows green "Connected")
2. Start a new conversation and ask Claude to use GitHub tools
3. Claude has no GitHub MCP tools available
4. search_mcp_registry with keywords ["github"] returns empty results

Troubleshooting attempted

• Disconnected and reconnected the GitHub connector
• Restarted the app entirely
• Started a fresh conversation — still no tools
• Gmail connector works fine in parallel

Expected behavior

GitHub connector should expose tools (e.g., list repos, view workflow runs, read issues/PRs) similar to how the Gmail connector exposes search_gmail_messages, read_gmail_message, etc.

Environment

• Claude Desktop (Cowork mode)
• macOS
• February 2026

Possibly related

• #18194 (MCP connectors returning 403 errors in Cowork)