### 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)

with create_session() as session:
            
            dag = dagbag.get_dag("test_example_bash_operator")
            dag.last_parsed_time = timezone.utcnow()
            dag.sync_to_db(processor_subdir=dag_directory)
            
            other_dag = other_dagbag.get_dag("test_start_date_scheduling")
            other_dag.last_parsed_time = timezone.utcnow()
            other_dag.sync_to_db(processor_subdir="other")
            
            stat = DagFileStat(
                num_dags=1,
                import_errors=0,
                last_finish_time=timezone.utcnow() + timedelta(hours=1),
                last_duration=1,
                run_count=1,
            )
            manager.processor._file_paths = [test_dag_path]
            manager.processor._file_stats[test_dag_path] = stat
            active_dag_count = session.query(func.count(DagModel.dag_id)).filter(DagModel.is_active).scalar()
            assert active_dag_count == 2
            manager.processor._scan_stale_dags()
            active_dag_count = session.query(func.count(DagModel.dag_id)).filter(DagModel.is_active).scalar()
            assert active_dag_count == 1
    @mock.patch(
        "airflow.dag_processing.processor.DagFileProcessorProcess.waitable_handle", new_callable=PropertyMock
    )
    @mock.patch("airflow.dag_processing.processor.DagFileProcessorProcess.pid", new_callable=PropertyMock)
    @mock.patch("airflow.dag_processing.processor.DagFileProcessorProcess.kill")
    def test_kill_timed_out_processors_kill(self, mock_kill, mock_pid, mock_waitable_handle):