Removing the unused instance variable notification_options from the server. A new variable is instantiated and initialized in init but never used. Instead fresh notification_options object is accepted as an argument in the create_initialization_options and get_capabilities functions.

Motivation and Context

This removes confusion about the use of notification_options in the server.

How Has This Been Tested?

Existing tests work as expected

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

None