Local processing job fails when wait=True (default)

**PySDK Version**
- [ ] PySDK V2 (2.x)
- [x] PySDK V3 (3.x)

**Describe the bug**
When running a FrameworkProcessor in local mode with wait=True (the default), the processing job completes successfully but then raises a ClientError when attempting to call DescribeProcessingJob on the AWS API. The job only exists locally, so the describe call fails with "Could not find requested job".

**To reproduce**
```python
from sagemaker.core import FrameworkProcessor
from sagemaker.core.helper.session_helper import Session
from sagemaker.core.image_uris import retrieve
from sagemaker.core.shapes import ProcessingInput, ProcessingOutput
from sagemaker.core.shapes import ProcessingS3Input, ProcessingS3Output
import os

region = Session().boto_region_name

processor_image_uri = retrieve(
framework="sklearn",
version="1.4-2",
region=region
)

processor = FrameworkProcessor(
image_uri=processor_image_uri,
role="arn:aws:iam::123456789012:role/DummyRole",
instance_type="local", # Local mode
instance_count=1,
base_job_name='test-local-processing',
command=["python3"]
)

# Create a simple test script
os.makedirs("./test_processing", exist_ok=True)
with open("./test_processing/test.py", "w") as f:
f.write("print('Processing complete')")

# Run with default wait=True
processor.run(
code="test.py",
source_dir="./test_processing",
inputs=[
ProcessingInput(
input_name="data",
s3_input=ProcessingS3Input(
s3_uri="file:///tmp/input",
local_path="/opt/ml/processing/input"
)
)
],
outputs=[
ProcessingOutput(
output_name="output",
s3_output=ProcessingS3Output(
s3_uri="file:///tmp/output",
local_path="/opt/ml/processing/output"
)
)
]
)
```

**Expected behavior**
The processing job should complete successfully without attempting to call the AWS DescribeProcessingJob API when running in local mode. The wait() method should recognize that the job is local and not try to refresh status.

**Screenshots or logs**
```
REDACTED-sagemaker-local exited with code 0
Compose Stopping Aborting on container exit...
Container REDACTED-sagemaker-local Stopping
Container REDACTED-sagemaker-local Stopped

[02/11/26 16:18:37] INFO ===== Job Complete ===== image.py:248

WARNING No region provided. Using default region. utils.py:340

INFO Runs on sagemaker prod, region:us-east-1 utils.py:354

╭─────────────────────────────── Traceback (most recent call last) ────────────────────────────────╮
│ in :30 │
│ │
│ 27 │ } │
│ 28 ) │
│ 29 │
│ ❱ 30 processor.run( │
│ 31 │ code="preprocessing.py", │
│ 32 │ source_dir="./processing", │
│ 33 │ requirements="requirements.txt", │
│ │
│ /opt/conda/lib/python3.12/site-packages/sagemaker/core/workflow/pipeline_context.py:346 in │
│ wrapper │
│ │
│ 343 │ │ │ │
│ 344 │ │ │ return _StepArguments(retrieve_caller_name(self_instance), run_func, *args, │
│ 345 │ │ │
│ ❱ 346 │ │ return run_func(*args, **kwargs) │
│ 347 │ │
│ 348 │ return wrapper │
│ 349 │
│ │
│ /opt/conda/lib/python3.12/site-packages/sagemaker/core/processing.py:1226 in run │
│ │
│ 1223 │ │ ) │
│ 1224 │ │ │
│ 1225 │ │ # Submit a processing job. │
│ ❱ 1226 │ │ return super().run( │
│ 1227 │ │ │ code=s3_runproc_sh, │
│ 1228 │ │ │ inputs=inputs, │
│ 1229 │ │ │ outputs=outputs, │
│ │
│ /opt/conda/lib/python3.12/site-packages/sagemaker/core/workflow/pipeline_context.py:346 in │
│ wrapper │
│ │
│ 343 │ │ │ │
│ 344 │ │ │ return _StepArguments(retrieve_caller_name(self_instance), run_func, *args, │
│ 345 │ │ │
│ ❱ 346 │ │ return run_func(*args, **kwargs) │
│ 347 │ │
│ 348 │ return wrapper │
│ 349 │
│ │
│ /opt/conda/lib/python3.12/site-packages/sagemaker/core/processing.py:843 in run │
│ │
│ 840 │ │ if not isinstance(self.sagemaker_session, PipelineSession): │
│ 841 │ │ │ self.jobs.append(self.latest_job) │
│ 842 │ │ │ if wait: │
│ ❱ 843 │ │ │ │ self.latest_job.wait(logs=logs) │
│ 844 │ │
│ 845 │ def _include_code_in_inputs(self, inputs, code, kms_key=None): │
│ 846 │ │ """Converts code to appropriate input and includes in input list. │
│ │
│ /opt/conda/lib/python3.12/site-packages/sagemaker/core/resources.py:143 in wrapper │
│ │
│ 140 │ │ @functools.wraps(func) │
│ 141 │ │ def wrapper(*args, **kwargs): │
│ 142 │ │ │ config = dict(arbitrary_types_allowed=True) │
│ ❱ 143 │ │ │ return validate_call(config=config)(func)(*args, **kwargs) │
│ 144 │ │ │
│ 145 │ │ return wrapper │
│ 146 │
│ │
│ /opt/conda/lib/python3.12/site-packages/pydantic/_internal/_validate_call.py:39 in │
│ wrapper_function │
│ │
│ 36 │ │ │
│ 37 │ │ @functools.wraps(wrapped) │
│ 38 │ │ def wrapper_function(*args, **kwargs): │
│ ❱ 39 │ │ │ return wrapper(*args, **kwargs) │
│ 40 │ │
│ 41 │ # We need to manually update this because `partial` object has no `__name__` and `__ │
│ 42 │ wrapper_function.__name__ = extract_function_name(wrapped) │
│ │
│ /opt/conda/lib/python3.12/site-packages/pydantic/_internal/_validate_call.py:136 in __call__ │
│ │
│ 133 │ │ if not self.__pydantic_complete__: │
│ 134 │ │ │ self._create_validators() │
│ 135 │ │ │
│ ❱ 136 │ │ res = self.__pydantic_validator__.validate_python(pydantic_core.ArgsKwargs(args, │
│ 137 │ │ if self.__return_pydantic_validator__: │
│ 138 │ │ │ return self.__return_pydantic_validator__(res) │
│ 139 │ │ else: │
│ │
│ /opt/conda/lib/python3.12/site-packages/sagemaker/core/resources.py:32145 in wait │
│ │
│ 32142 │ │ │ transient=True, │
│ 32143 │ │ ): │
│ 32144 │ │ │ while True: │
│ ❱ 32145 │ │ │ │ self.refresh() │
│ 32146 │ │ │ │ current_status = self.processing_job_status │
│ 32147 │ │ │ │ status.update(f"Current status: [bold]{current_status}") │
│ 32148 │
│ │
│ /opt/conda/lib/python3.12/site-packages/sagemaker/core/resources.py:143 in wrapper │
│ │
│ 140 │ │ @functools.wraps(func) │
│ 141 │ │ def wrapper(*args, **kwargs): │
│ 142 │ │ │ config = dict(arbitrary_types_allowed=True) │
│ ❱ 143 │ │ │ return validate_call(config=config)(func)(*args, **kwargs) │
│ 144 │ │ │
│ 145 │ │ return wrapper │
│ 146 │
│ │
│ /opt/conda/lib/python3.12/site-packages/pydantic/_internal/_validate_call.py:39 in │
│ wrapper_function │
│ │
│ 36 │ │ │
│ 37 │ │ @functools.wraps(wrapped) │
│ 38 │ │ def wrapper_function(*args, **kwargs): │
│ ❱ 39 │ │ │ return wrapper(*args, **kwargs) │
│ 40 │ │
│ 41 │ # We need to manually update this because `partial` object has no `__name__` and `__ │
│ 42 │ wrapper_function.__name__ = extract_function_name(wrapped) │
│ │
│ /opt/conda/lib/python3.12/site-packages/pydantic/_internal/_validate_call.py:136 in __call__ │
│ │
│ 133 │ │ if not self.__pydantic_complete__: │
│ 134 │ │ │ self._create_validators() │
│ 135 │ │ │
│ ❱ 136 │ │ res = self.__pydantic_validator__.validate_python(pydantic_core.ArgsKwargs(args, │
│ 137 │ │ if self.__return_pydantic_validator__: │
│ 138 │ │ │ return self.__return_pydantic_validator__(res) │
│ 139 │ │ else: │
│ │
│ /opt/conda/lib/python3.12/site-packages/sagemaker/core/resources.py:32025 in refresh │
│ │
│ 32022 │ │ logger.debug(f"Serialized input request: {operation_input_args}") │
│ 32023 │ │ │
│ 32024 │ │ client = Base.get_sagemaker_client() │
│ ❱ 32025 │ │ response = client.describe_processing_job(**operation_input_args) │
│ 32026 │ │ │
│ 32027 │ │ # deserialize response and update self │
│ 32028 │ │ transform(response, "DescribeProcessingJobResponse", self) │
│ │
│ /opt/conda/lib/python3.12/site-packages/botocore/client.py:602 in _api_call │
│ │
│ 599 │ │ │ │ │ f"{py_operation_name}() only accepts keyword arguments." │
│ 600 │ │ │ │ ) │
│ 601 │ │ │ # The "self" in this scope is referring to the BaseClient. │
│ ❱ 602 │ │ │ return self._make_api_call(operation_name, kwargs) │
│ 603 │ │ │
│ 604 │ │ _api_call.__name__ = str(py_operation_name) │
│ 605 │
│ │
│ /opt/conda/lib/python3.12/site-packages/botocore/context.py:123 in wrapper │
│ │
│ 120 │ │ │ with start_as_current_context(): │
│ 121 │ │ │ │ if hook: │
│ 122 │ │ │ │ │ hook() │
│ ❱ 123 │ │ │ │ return func(*args, **kwargs) │
│ 124 │ │ │
│ 125 │ │ return wrapper │
│ 126 │
│ │
│ /opt/conda/lib/python3.12/site-packages/botocore/client.py:1078 in _make_api_call │
│ │
│ 1075 │ │ │ │ 'error_code_override' │
│ 1076 │ │ │ ) or error_info.get("Code") │
│ 1077 │ │ │ error_class = self.exceptions.from_code(error_code) │
│ ❱ 1078 │ │ │ raise error_class(parsed_response, operation_name) │
│ 1079 │ │ else: │
│ 1080 │ │ │ return parsed_response │
│ 1081 │
╰──────────────────────────────────────────────────────────────────────────────────────────────────╯
ClientError: An error occurred (ValidationException) when calling the DescribeProcessingJob operation: Could not
find requested job with name: from-idea-to-prod-processing-2026-02-11-16-14-54-339
```

**System information**
A description of your system. Please provide:
- **SageMaker Python SDK version**: 3.4.1
- **Framework name (eg. PyTorch) or algorithm (eg. KMeans)**: sklearn (FrameworkProcessor)
- **Framework version**: 1.4-2
- **Python version**: 3.12
- **CPU or GPU**: CPU
- **Custom Docker image (Y/N)**: N

**Additional context**
The workaround is to set wait=False when calling processor.run() in local mode. However, this is not obvious to users.

Bắt đầu bằng cách tái hiện lần chạy FrameworkProcessor cục bộ với wait=True và kiểm tra luồng xử lý tại sagemaker/core/processing.py:843 cũng như phần triển khai wait tại sagemaker/core/resources.py:32145. Xác nhận rằng một job cục bộ đã hoàn tất sẽ tránh việc làm mới AWS DescribeProcessingJob, sau đó xác minh cùng hành vi này bằng ví dụ local-mode được cung cấp.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.