### 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)

"""Heartbeat DAG file processor and restart it if we are not done."""
        if not self._parent_signal_conn:
            raise ValueError("Process not started.")
        if self._process and not self._process.is_alive():
            self._process.join(timeout=0)
            if not self.done:
                self.log.warning(
                    "DagFileProcessorManager (PID=%d) exited with exit code %d - re-launching",
                    self._process.pid,
                    self._process.exitcode,
                )
                self.start()
        if self.done:
            return
        parsing_stat_age = time.monotonic() - self._last_parsing_stat_received_at
        if parsing_stat_age > self._processor_timeout.total_seconds():
            Stats.incr("dag_processing.manager_stalls")
            self.log.error(
                "DagFileProcessorManager (PID=%d) last sent a heartbeat %.2f seconds ago! Restarting it",
                self._process.pid,
                parsing_stat_age,
            )
            reap_process_group(self._process.pid, logger=self.log)
            self.start()
    def _sync_metadata(self, stat):