[BUG] MCP reconnection fails with different patterns for direct command vs interactive menu

Environment

• Platform (select one):
• [x] Anthropic API
• [ ] AWS Bedrock
• [ ] Google Vertex AI
• [ ] Other: <!-- specify -->
• Claude CLI version: 1.0.71 (Claude Code)
• Operating System: Linux (WSL2) - 6.6.87.2-microsoft-standard-WSL2
• Terminal: VSCode integrated terminal

Bug Description

Two different MCP reconnection methods exhibit different failure patterns:

1. Direct command (/mcp reconnect <server-name>): Shows "Successfully reconnected" but always disconnects immediately
2. Interactive menu (/mcp <server-name> → Reconnect): Fails on first attempt, succeeds on second attempt

The issue is reproducible with MCP's official Rust SDK example.

Steps to Reproduce

Setup: Build MCP's official Rust SDK counter example

# Clone the official MCP Rust SDK
git clone https://github.com/modelcontextprotocol/rust-sdk.git /tmp/rust-sdk
cd /tmp/rust-sdk

# Build the counter example
cargo build --example servers_counter_stdio

Configure Claude Code

Create or update .mcp.json in your project directory:

{
  "mcpServers": {
    "counter-test": {
      "command": "cargo",
      "args": ["run", "--manifest-path", "/tmp/rust-sdk/Cargo.toml", "--example", "servers_counter_stdio"]
    }
  }
}

Pattern A: Direct reconnect command

1. Start Claude Code in the project directory
2. Initial connection to counter-test succeeds
3. Use /mcp reconnect counter-test to reconnect
4. Claude Code displays "Successfully reconnected to counter-test"
5. However, the connection is immediately closed
6. Repeat /mcp reconnect counter-test multiple times
7. All attempts show "Successfully reconnected" but immediately disconnect

Pattern B: Interactive reconnect via menu

1. Start Claude Code in the project directory
2. Initial connection to counter-test succeeds
3. Use /mcp counter-test to open interactive menu
4. Select "Reconnect" option
5. Claude Code displays "Reconnected to counter-test." (note: different message)
6. First reconnection fails silently (connection is lost)
7. Repeat /mcp counter-test and select "Reconnect" again
8. Second reconnection succeeds and remains stable

Expected Behavior

MCP server reconnection should succeed on the first attempt.

Actual Behavior

• Direct command (/mcp reconnect counter-test): Always shows "Successfully reconnected to counter-test" but immediately disconnects
• Interactive menu (/mcp counter-test → Reconnect): First attempt fails silently, second attempt succeeds
• Different success messages indicate different code paths:
• Direct: "Successfully reconnected to counter-test" (misleading - connection always fails)
• Interactive: "Reconnected to counter-test." (accurate - but only on second attempt)
• Pattern is 100% reproducible

Additional Context

Workaround: Use /mcp counter-test and select Reconnect from the menu twice - the second attempt will succeed.
The direct /mcp reconnect counter-test command never works and should be avoided.