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