Add tests with new schema types
## Motivation and Context
<!-- Why is this change needed? What problem does it solve? -->
## How Has This Been Tested?
The repository currently contains duplicated tests:
- tests using the new schema
- tests using the old schema for compatibility checks. they will be
removed once the deprecation level is raised
## 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
- [x] Testing
## Checklist
- [x] I have read the [MCP
Documentation](https://modelcontextprotocol.io)
- [x] My code follows the repository's style guidelines
- [x] New and existing tests pass locally
- [x] I have added appropriate error handling
- [x] I have added or updated documentation as needed
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Co-authored-by: Konstantin Pavlov <1517853+kpavlov@users.noreply.github.com>
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