### 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)

curr_outlet_references.remove(ref)
                for d in dataset_outlets:
                    outlet_references[(task.dag_id, task.task_id)].add(d.uri)
                    outlet_datasets[DatasetModel.from_public(d)] = None
        all_datasets = outlet_datasets
        all_datasets.update(input_datasets)
        
        stored_datasets = {}
        for dataset in all_datasets:
            stored_dataset = session.scalar(
                select(DatasetModel).where(DatasetModel.uri == dataset.uri).limit(1)
            )
            if stored_dataset:
                
                
                
                stored_dataset.is_orphaned = expression.false()
                stored_datasets[stored_dataset.uri] = stored_dataset
            else:
                session.add(dataset)
                stored_datasets[dataset.uri] = dataset
        session.flush()  
        del all_datasets
        
        for dag_id, uri_list in dag_references.items():
            dag_refs_needed = {
                DagScheduleDatasetReference(dataset_id=stored_datasets[uri].id, dag_id=dag_id)
                for uri in uri_list
            }
            dag_refs_stored = set(