### 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)

"""Information about single processing of one file."""
    num_dags: int
    import_errors: int
    last_finish_time: datetime | None
    last_duration: timedelta | None
    run_count: int
class DagParsingSignal(enum.Enum):
    """All signals sent to parser."""
    AGENT_RUN_ONCE = "agent_run_once"
    TERMINATE_MANAGER = "terminate_manager"
    END_MANAGER = "end_manager"
class DagFileProcessorAgent(LoggingMixin, MultiprocessingStartMethodMixin):
    """
    Agent for DAG file processing.
    It is responsible for all DAG parsing related jobs in scheduler process.
    Mainly it can spin up DagFileProcessorManager in a subprocess,
    collect DAG parsing results from it and communicate signal/DAG parsing stat with it.
    This class runs in the main `airflow scheduler` process.
    :param dag_directory: Directory where DAG definitions are kept. All
        files in file_paths should be under this directory
    :param max_runs: The number of times to parse and schedule each file. -1
        for unlimited.
    :param processor_timeout: How long to wait before timing out a DAG file processor
    :param dag_ids: if specified, only schedule tasks with these DAG IDs
    :param pickle_dags: whether to pickle DAGs.
    :param async_mode: Whether to start agent in async mode
    """
    def __init__(