docs: Update README for client method usage

[stonexer]

Similar to #141. Fix Writing MCP Clients example in the README.

Motivation and Context

Update docs to match the latest types.

How Has This Been Tested?

Run the example.

Breaking Changes

No.

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