### 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)

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            if as_pk_tuple:
                tis_query = session.execute(tis).all()
                result.update(TaskInstanceKey(**cols._mapping) for cols in tis_query)
            else:
                result.update(ti.key for ti in session.scalars(tis))
            if exclude_task_ids is not None:
                result = {
                    task
                    for task in result
                    if task.task_id not in exclude_task_ids
                    and (task.task_id, task.map_index) not in exclude_task_ids
                }
        if as_pk_tuple:
            return result
        if result:
            
            ti_filters = TI.filter_for_tis(result)
            if ti_filters is not None:
                tis = select(TI).where(ti_filters)
        elif exclude_task_ids is None:
            pass  
        elif isinstance(next(iter(exclude_task_ids), None), str):
            tis = tis.where(TI.task_id.notin_(exclude_task_ids))
        else:
            tis = tis.where(not_(tuple_in_condition((TI.task_id, TI.map_index), exclude_task_ids)))
        return tis
    @provide_session
    def set_task_instance_state(