Sync the weather-server-python code with the documentation

[cr7258]

Motivation and Context

The Python MCP Server quickstart documentation has been updated to use FastMCP API, sync the weather-server-python with the documentation.

fixes #4

How Has This Been Tested?

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

[jspahrsummers]

Thank you!