Add stateless mode support for STDIO transport

[efj-amzn]

Motivation and Context

This change adds support for the stateless flag to STDIO transport, addressing issue #912. Currently, STDIO transport requires a full initialization handshake, making simple command line interactions like echo '{"jsonrpc":"2.0",...}' | python script.py impossible.

The stateless flag already exists for HTTP transport but was missing for STDIO. This feature is particularly helpful for:

• Simple CLI debugging and testing
• Support for older MCP clients that don't do the handshake
• Educational scenarios where users are learning about MCP without needing to understand the initialization protocol
• Quick command-line tool interactions

How Has This Been Tested?

Aside from the added tests, I created a basic server and ran some commands.

from mcp.server.fastmcp import FastMCP

# Create FastMCP server
mcp = FastMCP("StatelessTest")

# Register a simple echo tool
@mcp.tool()
def echo(message: str) -> str:
    """Echo a message back to the client."""
    return f"Echo: {message}"

if __name__ == "__main__":
    # Run in STDIO mode
    mcp.run()

% echo '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"echo","arguments":{"message":"Hello world"}}}' | FASTMCP_STATELESS_STDIO=true uv run test_stateless.py
[06/10/25 14:52:17] INFO     Processing request of type CallToolRequest                                                                                                                                                                                                                                                                          server.py:561
{"jsonrpc":"2.0","id":1,"result":{"content":[{"type":"text","text":"Echo: Hello world"}],"isError":false}}

% echo '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"echo","arguments":{"message":"Hello world"}}}' | FASTMCP_STATELESS_STDIO=false uv run test_stateless.py
<runtime exception>

Breaking Changes

None.

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

I forked from gitish 1a9ead0 and the tests occasionally hang on that commit.

Fixes #912

[ihrpr]

Thank you for contributing to the MCP Python SDK!

Statelessness only applies to the StreamableHttp transport, as the protocol itself is stateful and requires initialization. With StreamableHttp, the client must still initialize with one node before sending requests to any other nodes.
Given the protocol's emphasis on proper initialization handshakes, I don't believe introducing this complexity to STDIO is justified for testing purposes.