fix: refactor auth and improve error handling for Bedrock provider

Refactor to use auth_credential for consistent credential management and
improve error handling with defensive checks.

Changes:
- Use auth_credential instead of api_key for better credential handling
- Simplify model availability check to accept all pre-registered models
- Guard metrics collection when usage data is missing in responses
- Add debug logging for better troubleshooting of API issues
- Update unit tests for auth_credential refactoring

docs/docs/providers/inference/remote_bedrock.mdx

@@ -16,7 +16,7 @@ AWS Bedrock inference provider using OpenAI compatible endpoint.
 |-------|------|----------|---------|-------------|
 | `allowed_models` | `list[str \| None` | No |  | List of models that should be registered with the model registry. If None, all models are allowed. |
 | `refresh_models` | `<class 'bool'>` | No | False | Whether to refresh models periodically from the provider |
-| `api_key` | `str \| None` | No |  | Amazon Bedrock API key |
+| `api_key` | `pydantic.types.SecretStr \| None` | No |  | Authentication credential for the provider |
 | `region_name` | `<class 'str'>` | No | us-east-2 | AWS Region for the Bedrock Runtime endpoint |
 
 ## Sample Configuration