### 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)

"""Return source code for this DagCode object.
        :return: source code as string
        """
        return cls._get_code_from_db(fileloc)
    @staticmethod
    def _get_code_from_file(fileloc):
        with open_maybe_zipped(fileloc, "r") as f:
            code = f.read()
        return code
    @classmethod
    @provide_session
    def _get_code_from_db(cls, fileloc, session: Session = NEW_SESSION) -> str:
        dag_code = session.scalar(select(cls).where(cls.fileloc_hash == cls.dag_fileloc_hash(fileloc)))
        if not dag_code:
            raise DagCodeNotFound()
        else:
            code = dag_code.source_code
        return code
    @staticmethod
    def dag_fileloc_hash(full_filepath: str) -> int:
        """Hashing file location for indexing.
        :param full_filepath: full filepath of DAG file
        :return: hashed full_filepath
        """
        
        
        import hashlib
        
        return struct.unpack(">Q", hashlib.sha1(full_filepath.encode("utf-8")).digest()[-8:])[0] >> 8