### 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)

self._processors: dict[str, DagFileProcessorProcess] = {}
        self._num_run = 0
        
        self._file_stats: dict[str, DagFileStat] = {}
        
        self.last_dag_dir_refresh_time = timezone.make_aware(datetime.fromtimestamp(0))
        
        self.last_stat_print_time = 0
        
        self.last_deactivate_stale_dags_time = timezone.make_aware(datetime.fromtimestamp(0))
        
        self.parsing_cleanup_interval = conf.getint("scheduler", "parsing_cleanup_interval")
        
        self.stale_dag_threshold = conf.getint("scheduler", "stale_dag_threshold")
        
        self._processor_timeout = processor_timeout
        
        self.dag_dir_list_interval = conf.getint("scheduler", "dag_dir_list_interval")
        
        self._callback_to_execute: dict[str, list[CallbackRequest]] = defaultdict(list)
        self._log = logging.getLogger("airflow.processor_manager")
        self.waitables: dict[Any, MultiprocessingConnection | DagFileProcessorProcess] = (
            {
                self._direct_scheduler_conn: self._direct_scheduler_conn,
            }
            if self._direct_scheduler_conn is not None
            else {}
        )
        self.heartbeat: Callable[[], None] = lambda: None
    def register_exit_signals(self):