HTTP-based MCP server tools not available to model despite showing "Running" status

Description

When an MCP server is configured with "type": "http" (Streamable HTTP transport), the Claude Code UI shows the server as "Running" with the correct tool and prompt count, but those tools are not injected into the model's context and cannot be called.

Steps to Reproduce

1. Add a remote HTTP MCP server to .mcp.json:

``json
{
"mcpServers": {
"cloudflare-docs": {
"type": "http",
"url": "https://docs.mcp.cloudflare.com/mcp"
}
}
}
``

1. Open the /mcp panel and click "Start" on the server
2. Verify the UI shows Running | 2 tools | 1 prompts
3. Ask Claude to use one of the server's tools (or use ToolSearch to look for them)

Expected Behavior

The server's tools are available to the model and can be invoked.

Actual Behavior

Tools are not available to the model. ToolSearch returns no results for the server's tools. The model falls back to training knowledge instead of querying the MCP server.

Environment

• Platform: macOS 23.6.0
• Claude Code version: (check with claude --version)
• Transport type: http (Streamable HTTP — also reproduced with "type": "sse" prior to switching)

Additional Context

Stdio-based MCP servers in the same .mcp.json do not exhibit this issue. The problem appears specific to remote HTTP transport servers.