### Apache Airflow version

2.6.3

### What happened

When running multiple standalone DAG processors with separate DAG directories using the `--subdir` argument the processors keep deactivating each other's DAGs (and reactivating their own).

After stepping through the code with a debugger I think the issue is that the calls [here](https://github.com/apache/airflow/blob/2.6.3/airflow/dag_processing/manager.py#L794) and [here](https://github.com/apache/airflow/blob/2.6.3/airflow/dag_processing/manager.py#L798) have no awareness of the DAG directories.

### What you think should happen instead

The DAG processors should not touch each other's DAGs in the metadata DB.

### How to reproduce

Start two or more standalone DAG processors with separate DAG directories and observe (e.g. via the UI) how the list of active DAGs keeps changing constantly.

### Operating System

Linux 94b223524983 6.1.32-0-virt #1-Alpine SMP PREEMPT_DYNAMIC Mon, 05 Jun 2023 09:39:09 +0000 x86_64 x86_64 x86_64 GNU/Linux

### Versions of Apache Airflow Providers

_No response_

### Deployment

Other Docker-based deployment

### Deployment details

_No response_

### Anything else

_No response_

### Are you willing to submit PR?

- [ ] 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,
        start_date: datetime | None = None,
        end_date: datetime | None = None,
        state: list[TaskInstanceState] | None = None,
        session: Session = NEW_SESSION,
    ) -> list[TaskInstance]:
        if not start_date:
            start_date = (timezone.utcnow() - timedelta(30)).replace(
                hour=0, minute=0, second=0, microsecond=0
            )
        query = self._get_task_instances(
            task_ids=None,
            start_date=start_date,
            end_date=end_date,
            run_id=None,
            state=state or (),
            include_subdags=False,
            include_parentdag=False,
            include_dependent_dags=False,
            exclude_task_ids=(),
            session=session,
        )
        return session.scalars(cast(Select, query).order_by(DagRun.execution_date)).all()
    @overload
    def _get_task_instances(