Connecting MCP to Zed client finds zero tools

[fredkzk]

Hi,
My Zed IDE can't find the tools from your mcp server whether I set it up with "transport": "http" or without it.
Example following Zed's own template:

{
  /// Configure an MCP server that you connect to over HTTP
  ///
  /// The name of your remote MCP server
  "specification-website": {
    /// The URL of the remote MCP server
    "url": "https://mcp.specification.website/mcp",
    /// Uncomment to use a pre-registered OAuth client. You can include the client secret here as well, otherwise it will be prompted interactively and saved in the system keychain.
    // "oauth": {
    //   "client_id": "your-client-id",
    // },
    "headers": {
     /// Any headers to send along
     // "Authorization": "Bearer <token>
    }
  }
}

Zed does confirm a successful configuration, yet no tools available.
How to set it up correctly please?