Addresses an issue where thinking signature validation fails due to model mapping and empty internal registry.
- Implements a fallback mechanism in the router to use the global model registry when the internal registry is empty. This ensures that models registered via API keys are correctly resolved even without local provider configurations.
- Modifies `GetModelGroup` to use registry-based grouping in addition to name pattern matching, covering cases where models are registered with API keys but lack provider names in their names.
- Updates signature validation to compare model groups instead of exact model names.
These changes resolve thinking signature validation errors and improve the accuracy of model resolution.
