Add exception type to error responses in chat and completion endpoints

[adambalogh]

Summary

Enhanced error responses across chat and completion endpoints to include the exception type, improving debugging and error handling visibility.

Key Changes

• Chat Controller (_create_non_streaming_response): Added exception_type field to non-streaming error responses
• Chat Controller (_create_streaming_response): Added exception_type field to streaming error responses and stream setup error responses
• Completions Controller (create_completion): Added exception_type field to completion error responses

Implementation Details

• All error responses now include exception_type: type(e).__name__ alongside the existing error message
• This change applies to three error handling paths:
  1. Non-streaming chat completions
  2. Streaming chat completions (both stream generation and setup phases)
  3. Text completions
• The exception type is extracted using Python's built-in type(e).__name__ to provide the class name of the caught exception
• Logging behavior remains unchanged; only the response payload is enhanced