### 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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        result: set[TaskInstanceKey] = set()
        
        if as_pk_tuple:
            tis = select(TI.dag_id, TI.task_id, TI.run_id, TI.map_index)
        else:
            tis = select(TaskInstance)
        tis = tis.join(TaskInstance.dag_run)
        if include_subdags:
            
            conditions = []
            for dag in self.subdags + [self]:
                conditions.append(
                    (TaskInstance.dag_id == dag.dag_id) & TaskInstance.task_id.in_(dag.task_ids)
                )
            tis = tis.where(or_(*conditions))
        elif self.partial:
            tis = tis.where(TaskInstance.dag_id == self.dag_id, TaskInstance.task_id.in_(self.task_ids))
        else:
            tis = tis.where(TaskInstance.dag_id == self.dag_id)
        if run_id:
            tis = tis.where(TaskInstance.run_id == run_id)
        if start_date:
            tis = tis.where(DagRun.execution_date >= start_date)
        if task_ids is not None:
            tis = tis.where(TaskInstance.ti_selector_condition(task_ids))