docs: fix code example in README.md

[phimage]

While testing, I copied some README.md files and noticed several issues. I’d like to contribute by helping to fix them.

Motivation and Context

• Code evolves quickly, so some examples may no longer work.
• Having copy-pasteable code will help developers who are just getting started with this SDK.

How Has This Been Tested?

I’ve extracted all the code snippets into Swift files and was able to build them without issues.

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