### Apache Airflow version

main (development)

### What happened

When dag processor starts with a sub directory to process then the import errors are recorded with that path. So when there is processor for airflow-dag-processor-0 folder in order to remove import errors it lists all files under airflow-dag-processor-0 folder and deletes those not present. This becomes an issue when there is airflow-dag-processor-1 that records import errors whose files won't be part of airflow-dag-processor-0 folder. 

### What you think should happen instead

The fix would be to have processor_subdir stored in ImportError table so that during querying we only look at import errors relevant to the dag processor and don't delete other items. A fix similar to https://github.com/apache/airflow/pull/33357 needs to be applied for import errors as well.

### How to reproduce

1. create a dag file with import error at `~/airflow/dags/airflow-dag-processor-0/sample_sleep.py` . Start a dag processor with -S to process "~/airflow/dags/airflow-dag-processor-0/" . Import error should be present.
2. create a dag file with import error at `~/airflow/dags/airflow-dag-processor-1/sample_sleep.py` . Start a dag processor with -S to process "~/airflow/dags/airflow-dag-processor-1/". Import error for airflow-dag-processor-0 is deleted.
3. 

```python
from datetime import datetime, timedelta

from airflow import DAG
from airflow.decorators import task

from datetime import timedelta, invalid


with DAG(
    dag_id="task_duration",
    start_date=datetime(2023, 1, 1),
    catchup=True,
    schedule_interval="@daily",
) as dag:

    @task
    def sleeper():
        pass

    sleeper()
```

### Operating System

Ubuntu

### Versions of Apache Airflow Providers

_No response_

### Deployment

Virtualenv installation

### Deployment details

_No response_

### Anything else

_No response_

### Are you willing to submit PR?

- [X] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

"""Time when this started to process the file."""
        if self._start_time is None:
            raise AirflowException("Tried to get start time before it started!")
        return self._start_time
    @property
    def waitable_handle(self):
        return self._process.sentinel
    def import_modules(self, file_path: str | Iterable[str]):
        def _import_modules(filepath):
            for module in iter_airflow_imports(filepath):
                try:
                    importlib.import_module(module)
                except Exception as e:
                    
                    
                    self.log.warning(
                        "Error when trying to pre-import module '%s' found in %s: %s",
                        module,
                        file_path,
                        e,
                    )
        if isinstance(file_path, str):
            _import_modules(file_path)
        elif isinstance(file_path, Iterable):
            for path in file_path:
                _import_modules(path)
class DagFileProcessor(LoggingMixin):