[Doc] Tweak stdio transport example code in the README

[koic]

Motivation and Context

The example code is located at ./examples/stdio_server.rb. Also, the content provided as input via stdio has been updated to avoid returning an error data. Using ping pong as an example, here's the difference:

Before

An error data is returned.

$ ./examples/stdio_server.rb
{"jsonrpc":"2.0","id":"1","result":"pong"}
{"jsonrpc":"2.0","id":null,"error":{"code":-32600,"message":"Invalid Request","data":"Method name must be a string and not start with \"rpc.\""}}

This error message is generated in the following location:
https://github.com/Shopify/json-rpc-handler/blob/v0.1.1/lib/json_rpc_handler.rb#L70

After

The expected result is returned without error data.

$ ./examples/stdio_server.rb
{"jsonrpc":"2.0","id":"1","method":"ping"}
{"jsonrpc":"2.0","id":"1","result":{}}

The other stdin example has been updated to use data that does not cause errors.
With this document update, users can verify the behavior of the MCP server via stdin without using an MCP client.

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