FrameworkProcessor wait/describe doesn't respect region

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

**Describe the bug**

`FrameworkProcessor` respects a region provided via `sagemaker_session.boto_session` when creating the job, but then ignores it when attempting to call `DescribeProcessingJob` for monitoring when `wait=True`.

**To reproduce**

Create any processing job in a **different region from your current/default**, as follows, and run it with `wait=True`:

```python
import boto3
from sagemaker.core.helper.session_helper import Session as SageMakerSession
from sagemaker.core.processing import FrameworkProcessor

sagemaker_sess = SageMakerSession(
# Anywhere that ISN'T your current default/active region:
boto_session=boto3.Session(region_name="ap-southeast-1"),
)
pytorch_processor = FrameworkProcessor(
sagemaker_session=sagemaker_sess,
...
)

pytorch_processor.run(
wait=True,
...
)
```

For example could consider adjusting [this walkthrough sample](https://sagemaker.readthedocs.io/en/stable/v3-examples/ml-ops-examples/v3-processing-job-pytorch/v3-pytorch-processing-example.html).

**Expected behavior**

The job runs in the explicitly specified region (`ap-southeast-1` above), and tails logs as usual for `wait=True`

**Actual behavior**

The job starts just fine, but the SDK immediately exits with an error because it tries to call `DescribeProcessingJob` in the current default region - not the one where the job was started.

**Screenshots or logs**

```
[04/24/26 23:37:57] INFO Creating processing-job with name glm-47--2026-0424-18-07-54 [processing.py](file:///.../.venv/lib/python3.12/site-packages/sagemaker/core/processing.py):[612](file:///.../.venv/lib/python3.12/site-packages/sagemaker/core/processing.py#612)
╭─────────────────────────────── Traceback (most recent call last) ────────────────────────────────╮
│ in :70 │
│ │
│ 67 time_suffix = strftime("%Y-%m%d-%H-%M-%S", gmtime()) │
│ 68 job_name = "--".join((model_id_namepart, time_suffix)) │
│ 69 │
│ ❱ 70 pytorch_processor.run( │
│ 71 │ code="main.py", │
│ 72 │ source_dir=os.path.abspath("code"), │
│ 73 │ job_name=job_name, │
│ │
│ /.../.venv/lib/python3.12/site-packages/sagemaker/core/workflow/pipeline_c │
│ ontext.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 │
│ │
│ /.../.venv/lib/python3.12/site-packages/sagemaker/core/processing.py:1229 │
│ in run │
│ │
│ 1226 │ │ ) │
│ 1227 │ │ │
│ 1228 │ │ # Submit a processing job. │
│ ❱ 1229 │ │ return super().run( │
│ 1230 │ │ │ code=s3_runproc_sh, │
│ 1231 │ │ │ inputs=inputs, │
│ 1232 │ │ │ outputs=outputs, │
│ │
│ /....venv/lib/python3.12/site-packages/sagemaker/core/workflow/pipeline_c │
│ ontext.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 │
│ │
│ /.../.venv/lib/python3.12/site-packages/sagemaker/core/processing.py:846 │
│ in run │
│ │
│ 843 │ │ if not isinstance(self.sagemaker_session, PipelineSession): │
│ 844 │ │ │ self.jobs.append(self.latest_job) │
│ 845 │ │ │ if wait: │
│ ❱ 846 │ │ │ │ self.latest_job.wait(logs=logs) │
│ 847 │ │
│ 848 │ def _include_code_in_inputs(self, inputs, code, kms_key=None): │
│ 849 │ │ """Converts code to appropriate input and includes in input list. │
│ │
│ /.../.venv/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 │
│ │
│ /.../.venv/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) │
│ │
│ /.../.venv/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: │
│ │
│ /.../.venv/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 │
│ │
│ /.../.venv/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 │
│ │
│ /.../.venv/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) │
│ │
│ /.../.venv/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: │
│ │
│ /.../.venv/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) │
│ │
│ /.../.venv/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 │
│ │
│ /.../.venv/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 │
│ │
│ /.../.venv/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: glm-47--2026-0424-18-07-54
```

**System information**
A description of your system. Please provide:
- **SageMaker Python SDK version**: `sagemaker-core` v2.6.0
- **Framework name (eg. PyTorch) or algorithm (eg. KMeans)**: PyTorch
- **Framework version**: 2.8
- **Python version**: 3.12
- **CPU or GPU**: CPU
- **Custom Docker image (Y/N)**: N

**Additional context**

N/A

Bắt đầu bằng cách lần theo FrameworkProcessor.run trong sagemaker/core/processing.py qua latest_job.wait, sau đó kiểm tra đường dẫn refresh của tài nguyên processing-job trong sagemaker/core/resources.py. Tái hiện vấn đề bằng một boto3 session được đặt thành ap-southeast-1 trong khi region mặc định khác với region này. Hoàn tất có nghĩa là wait=True giám sát và theo dõi job trong region được cấu hình rõ ràng mà không gặp lỗi DescribeProcessingJob.

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