### 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)

"""
        Test that DagModel.next_dagrun_create_after is set to NULL when the dag cannot be created due to max
        active runs being hit.
        """
        dag = DAG(dag_id="test_scheduler_verify_max_active_runs", start_date=DEFAULT_DATE)
        dag.max_active_runs = 1
        EmptyOperator(task_id="dummy", dag=dag, owner="airflow")
        session = settings.Session()
        dag.clear()
        DAG.bulk_write_to_db([dag], session=session)
        model = session.get(DagModel, dag.dag_id)
        assert model.next_dagrun == DEFAULT_DATE
        assert model.next_dagrun_create_after == DEFAULT_DATE + timedelta(days=1)
        dr = dag.create_dagrun(
            state=state,
            execution_date=model.next_dagrun,
            run_type=DagRunType.SCHEDULED,
            session=session,
        )
        assert dr is not None
        DAG.bulk_write_to_db([dag])
        model = session.get(DagModel, dag.dag_id)
        
        assert model.next_dagrun_create_after is None
        
        DAG.bulk_write_to_db([dag])
        model = session.get(DagModel, dag.dag_id)
        assert model.next_dagrun_create_after is None
    def test_bulk_write_to_db_has_import_error(self):