[refactor(client)] Remove unused variable

[ftnext]

Same as modelcontextprotocol/docs#172

Motivation and Context

The client program will work even if the variable tool_results is removed

How Has This Been Tested?

I wrote a client in Python according to the quickstart and executed it to work.
https://gist.github.com/ftnext/9988e2f9929f836557091012b4160061

Breaking Changes

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

Additional context