### 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)

"""Create a Timetable instance from a ``schedule_interval`` argument."""
    if interval is NOTSET:
        return DeltaDataIntervalTimetable(DEFAULT_SCHEDULE_INTERVAL)
    if interval is None:
        return NullTimetable()
    if interval == "@once":
        return OnceTimetable()
    if interval == "@continuous":
        return ContinuousTimetable()
    if isinstance(interval, (timedelta, relativedelta)):
        return DeltaDataIntervalTimetable(interval)
    if isinstance(interval, str):
        return CronDataIntervalTimetable(interval, timezone)
    raise ValueError(f"{interval!r} is not a valid schedule_interval.")
def get_last_dagrun(dag_id, session, include_externally_triggered=False):
    """
    Return the last dag run for a dag, None if there was none.
    Last dag run can be any type of run e.g. scheduled or backfilled.
    Overridden DagRuns are ignored.
    """
    DR = DagRun
    query = select(DR).where(DR.dag_id == dag_id)
    if not include_externally_triggered:
        query = query.where(DR.external_trigger == expression.false())
    query = query.order_by(DR.execution_date.desc())
    return session.scalar(query.limit(1))
def get_dataset_triggered_next_run_info(