### 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)

"""Whether all files been processed at least once."""
        return self._all_files_processed
    def terminate(self):
        """Send termination signal to DAG parsing processor manager to terminate all DAG file processors."""
        if self._process and self._process.is_alive():
            self.log.info("Sending termination message to manager.")
            try:
                self._parent_signal_conn.send(DagParsingSignal.TERMINATE_MANAGER)
            except ConnectionError:
                pass
    def end(self):
        """Terminate (and then kill) the manager process launched."""
        if not self._process:
            self.log.warning("Ending without manager process.")
            return
        
        
        
        self._process.join(timeout=1.0)
        reap_process_group(self._process.pid, logger=self.log)
        self._parent_signal_conn.close()
class DagFileProcessorManager(LoggingMixin):
    """
    Manage processes responsible for parsing DAGs.
    Given a list of DAG definition files, this kicks off several processors
    in parallel to process them and put the results to a multiprocessing.Queue
    for DagFileProcessorAgent to harvest. The parallelism is limited and as the
    processors finish, more are launched. The files are processed over and
    over again, but no more often than the specified interval.
    :param dag_directory: Directory where DAG definitions are kept. All