fix: Include extra field for context log

[vincent0426]

Allow extra field within context log

without extra:

{
  "method": "notifications/message",
  "params": {
    "level": "info",
    "data": "test message"
  }
}

with extra:

{
  "method": "notifications/message",
  "params": {
    "level": "info",
    "data": {
      "message": "test message",
      "additional_string": "example",
      "additional_number": 123,
      "additional_boolean": true,
      "additional_list": [
        "a",
        "b",
        "c"
      ],
      "additional_dict": {
        "a": 1,
        "b": 2,
        "c": 3
      },
      "additional_null": null
    }
  }
}

Motivation and Context

Closes #565

How Has This Been Tested?

Unit test, manual test with inspector

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