### 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)

secrets_backend_list.pop(0)
        return dr
    @provide_session
    def create_dagrun(
        self,
        state: DagRunState,
        execution_date: datetime | None = None,
        run_id: str | None = None,
        start_date: datetime | None = None,
        external_trigger: bool | None = False,
        conf: dict | None = None,
        run_type: DagRunType | None = None,
        session: Session = NEW_SESSION,
        dag_hash: str | None = None,
        creating_job_id: int | None = None,
        data_interval: tuple[datetime, datetime] | None = None,
    ):
        """
        Create a dag run from this dag including the tasks associated with this dag.
        Returns the dag run.
        :param run_id: defines the run id for this dag run
        :param run_type: type of DagRun
        :param execution_date: the execution date of this dag run
        :param state: the state of the dag run
        :param start_date: the date this dag run should be evaluated
        :param external_trigger: whether this dag run is externally triggered
        :param conf: Dict containing configuration/parameters to pass to the DAG
        :param creating_job_id: id of the job creating this DagRun
        :param session: database session