### 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)

self._fetch_callbacks_with_retries(max_callbacks, session)
    @retry_db_transaction
    def _fetch_callbacks_with_retries(self, max_callbacks: int, session: Session):
        """Fetch callbacks from database and add them to the internal queue for execution."""
        self.log.debug("Fetching callbacks from the database.")
        with prohibit_commit(session) as guard:
            query = session.query(DbCallbackRequest)
            if self.standalone_dag_processor:
                query = query.filter(
                    DbCallbackRequest.processor_subdir == self.get_dag_directory(),
                )
            query = query.order_by(DbCallbackRequest.priority_weight.asc()).limit(max_callbacks)
            callbacks = with_row_locks(
                query, of=DbCallbackRequest, session=session, **skip_locked(session=session)
            ).all()
            for callback in callbacks:
                try:
                    self._add_callback_to_queue(callback.get_callback_request())
                    session.delete(callback)
                except Exception as e:
                    self.log.warning("Error adding callback for execution: %s, %s", callback, e)
            guard.commit()
    def _add_callback_to_queue(self, request: CallbackRequest):