[BUG] Claude Code MCP Servers not compatible with Claude Desktop

I am running Claude Code 1.0.44 AND Claude Desktop 0.11.6.

Please help me out on discrepancies. What am I missing. The documentation is not exactly clear here. I was expect some degree of parity.

😄 This works well:

• Claude Code works like this claude mcp add -t http my_mcp http://localhost:8080
• Claude Code works like this (contents of my .mcp.json)

{
  "mcpServers": {
    "my_mcp": {
      "type": "http",
      "url": "http://localhost:8080"
    }
  }
}

😦 Claude Desktop

But this one doesn't in Claude Desktop, and I do not know why. It perpetually says "Connect" even though I have clicked connect. Can you provide an assist:

<img width="775" height="230" alt="Image" src="https://github.com/user-attachments/assets/5c89aae9-bcc3-4f95-bd3d-873e98087983" />

😦 Claude.AI On The Web

This one also is not working when I click "Connect"

<img width="527" height="100" alt="Image" src="https://github.com/user-attachments/assets/9486f067-c5f7-42f6-87d0-2d23c557c47d" />