fix: improve client type identification with test coverage

[ShaneOxM]

Fix TypeScript Client Type Identification

Relates to:

Fixes TypeScript error in client initialization where name property is incorrectly assumed to exist on Client type.

Risks

Low - This is a type-safety improvement with comprehensive test coverage. Changes are isolated to client type identification logic.

Background

What does this PR do?

• Adds a robust determineClientType helper function for reliable client identification
• Fixes TypeScript errors in client initialization
• Adds comprehensive test suite for client type identification
• Improves debugging with additional logging

What kind of change is this?

Bug fixes (non-breaking change which fixes an issue)

• Resolves TypeScript type error
• Maintains backward compatibility
• Improves type safety

Documentation changes needed?

My changes do not require a change to the project documentation.
The changes are internal implementation details that don't affect the public API.

Testing

Where should a reviewer start?

1. Review the determineClientType function in agent/src/index.ts
2. Check the test cases in agent/src/__tests__/client-type-identification.test.ts
3. Verify the TypeScript error is resolved

Detailed testing steps

1. Run pnpm test in the agent directory to verify all tests pass
2. Tests cover three scenarios:
   • Clients with explicit type property
   • Clients with constructor name identification
   • Plain object clients with fallback identifiers