### 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)

dag = DAG("test_schedule_interval_arg", schedule_interval="*/5 * * * *")
        assert dag.timetable == cron_timetable("*/5 * * * *")
        assert dag.schedule_interval == "*/5 * * * *"
        assert dag.timetable.description == "Every 5 minutes"
    def test_timetable_still_works(self):
        dag = DAG("test_schedule_interval_arg", timetable=cron_timetable("*/6 * * * *"))
        assert dag.timetable == cron_timetable("*/6 * * * *")
        assert dag.schedule_interval == "*/6 * * * *"
        assert dag.timetable.description == "Every 6 minutes"
    @pytest.mark.parametrize(
        "timetable, expected_description",
        [
            (NullTimetable(), "Never, external triggers only"),
            (cron_timetable("0 0 * * *"), "At 00:00"),
            (cron_timetable("@daily"), "At 00:00"),
            (cron_timetable("0 0 * * 0"), "At 00:00, only on Sunday"),
            (cron_timetable("@weekly"), "At 00:00, only on Sunday"),
            (cron_timetable("0 0 1 * *"), "At 00:00, on day 1 of the month"),
            (cron_timetable("@monthly"), "At 00:00, on day 1 of the month"),
            (cron_timetable("0 0 1 */3 *"), "At 00:00, on day 1 of the month, every 3 months"),
            (cron_timetable("@quarterly"), "At 00:00, on day 1 of the month, every 3 months"),
            (cron_timetable("0 0 1 1 *"), "At 00:00, on day 1 of the month, only in January"),
            (cron_timetable("@yearly"), "At 00:00, on day 1 of the month, only in January"),
            (cron_timetable("5 0 * 8 *"), "At 00:05, only in August"),
            (OnceTimetable(), "Once, as soon as possible"),
            (delta_timetable(datetime.timedelta(days=1)), ""),
            (cron_timetable("30 21 * * 5 1"), ""),
        ],
    )
    def test_description_from_timetable(self, timetable, expected_description):