### 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)

async_mode=True,
            ),
        )
        manager.processor._run_parsing_loop()
        result = None
        while parent_pipe.poll(timeout=None):
            result = parent_pipe.recv()
            if isinstance(result, DagParsingStat) and result.done:
                break
        
        assert sum(stat.run_count for stat in manager.processor._file_stats.values()) == 3
        with create_session() as session:
            assert session.get(DagModel, dag_id) is not None
    @conf_vars({("core", "load_examples"): "False"})
    @pytest.mark.backend("mysql", "postgres")
    @pytest.mark.execution_timeout(30)
    @mock.patch("airflow.dag_processing.manager.DagFileProcessorProcess")
    def test_pipe_full_deadlock(self, mock_processor):
        dag_filepath = TEST_DAG_FOLDER / "test_scheduler_dags.py"
        child_pipe, parent_pipe = multiprocessing.Pipe()
        
        for fd in (parent_pipe.fileno(),):
            sock = socket.socket(fileno=fd)
            sock.setsockopt(socket.SOL_SOCKET, socket.SO_SNDBUF, 1024)
            sock.setsockopt(socket.SOL_SOCKET, socket.SO_RCVBUF, 1024)
            sock.detach()
        exit_event = threading.Event()
        
        
        def keep_pipe_full(pipe, exit_event):