### 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)

start_dates = [t.start_date for t in self.tasks if t.start_date]
        if self.start_date is not None:
            start_dates.append(self.start_date)
        earliest = None
        if start_dates:
            earliest = timezone.coerce_datetime(min(start_dates))
        latest = self.end_date
        end_dates = [t.end_date for t in self.tasks if t.end_date]
        if len(end_dates) == len(self.tasks):  
            if self.end_date is not None:
                end_dates.append(self.end_date)
            if end_dates:
                latest = timezone.coerce_datetime(max(end_dates))
        return TimeRestriction(earliest, latest, self.catchup)
    def iter_dagrun_infos_between(
        self,
        earliest: pendulum.DateTime | None,
        latest: pendulum.DateTime,
        *,
        align: bool = True,
    ) -> Iterable[DagRunInfo]:
        """Yield DagRunInfo using this DAG's timetable between given interval.
        DagRunInfo instances yielded if their ``logical_date`` is not earlier
        than ``earliest``, nor later than ``latest``. The instances are ordered
        by their ``logical_date`` from earliest to latest.
        If ``align`` is ``False``, the first run will happen immediately on
        ``earliest``, even if it does not fall on the logical timetable schedule.