### 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)

file_last_changed: dict[str, datetime], import_errors: dict[str, str], session: Session = NEW_SESSION
    ) -> None:
        """
        Update any import errors to be displayed in the UI.
        For the DAGs in the given DagBag, record any associated import errors and clears
        errors for files that no longer have them. These are usually displayed through the
        Airflow UI so that users know that there are issues parsing DAGs.
        :param dagbag: DagBag containing DAGs with import errors
        :param session: session for ORM operations
        """
        files_without_error = file_last_changed - import_errors.keys()
        
        
        for dagbag_file in files_without_error:
            session.execute(
                delete(errors.ImportError)
                .where(errors.ImportError.filename.startswith(dagbag_file))
                .execution_options(synchronize_session="fetch")
            )
        
        existing_import_error_files = [x.filename for x in session.query(errors.ImportError.filename).all()]
        
        for filename, stacktrace in import_errors.items():
            if filename in existing_import_error_files:
                session.query(errors.ImportError).filter(errors.ImportError.filename == filename).update(
                    {"filename": filename, "timestamp": timezone.utcnow(), "stacktrace": stacktrace},
                    synchronize_session="fetch",