Claude Code MCP Server won't Expose Tools to Claude Desktop

Claude Code won't expose any tools to Claude Desktop:

{
  "mcpServers": {

    "claude-code": {
      "command": "npx",
      "args": [
        "@anthropic-ai/claude-code"
      ]
    },

    "claude-code-2": {
      "command": "npx",
      "args": [
        "@anthropic-ai/claude-code",
        "mcp serve"
      ]
    }

  }
}

<img width="768" alt="Image" src="https://github.com/user-attachments/assets/c66d50ae-5f69-425f-a188-136a81527d48" />

<img width="774" alt="Image" src="https://github.com/user-attachments/assets/d5e05f20-a157-4612-904b-81b9093bb2b0" />

However using the MCP inspector, it works:

!Image

---

> claude /doctor

╭────────────────────────────────────────────╮
│ ✻ Welcome to Claude Code research preview! │
│                                            │
│   /help for help                           │
│                                            │
│   cwd: /Users/christo/mcp                  │
╰────────────────────────────────────────────╯

 ✓ npm permissions: OK

 Your installation is healthy and ready for auto-updates.

 Press Enter to continue…

> claude config list

{
  "dontCrawlDirectory": false,
  "enableArchitectTool": false,
  "hasTrustDialogAccepted": true,
  "hasCompletedProjectOnboarding": true,
  "ignorePatterns": [
    ".aider*"
  ]
}

> claude -v

0.2.29 (Claude Code)