### 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,
        base_date: datetime,
        num: int,
        *,
        session: Session = NEW_SESSION,
    ) -> list[TaskInstance]:
        """Get ``num`` task instances before (including) ``base_date``.
        The returned list may contain exactly ``num`` task instances
        corresponding to any DagRunType. It can have less if there are
        less than ``num`` scheduled DAG runs before ``base_date``.
        """
        execution_dates: list[Any] = session.execute(
            select(DagRun.execution_date)
            .where(
                DagRun.dag_id == self.dag_id,
                DagRun.execution_date <= base_date,
            )
            .order_by(DagRun.execution_date.desc())
            .limit(num)
        ).all()
        if len(execution_dates) == 0:
            return self.get_task_instances(start_date=base_date, end_date=base_date, session=session)
        min_date: datetime | None = execution_dates[-1]._mapping.get(
            "execution_date"
        )  
        return self.get_task_instances(start_date=min_date, end_date=base_date, session=session)
    @provide_session
    def get_task_instances(