fix: Support updating output schema

[vincent0426]

Closes #884

Motivation and Context

Fix the issue to support updating the output schema.

How Has This Been Tested?

Added a test for updating the output schema

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