### 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, fileloc, expected_relative, session, clear_dags, reader_dags_folder
    ):
        """
        The serialized dag model includes the dags folder as configured on the thing serializing
        the dag.  On the thing deserializing the dag, when determining relative fileloc,
        we should use the dags folder of the processor.  So even if the dags folder of
        the deserializer is different (meaning that the full path is no longer relative to
        the dags folder) then we should still get the relative fileloc as it existed on the
        serializer process.  When the full path is not relative to the configured dags folder,
        then relative fileloc should just be the full path.
        """
        dag = DAG(dag_id="test")
        dag.fileloc = fileloc
        sdm = SerializedDagModel(dag)
        session.add(sdm)
        session.commit()
        session.expunge_all()
        sdm = SerializedDagModel.get(dag.dag_id, session)
        dag = sdm.dag
        with conf_vars({("core", "dags_folder"): reader_dags_folder}):
            assert dag.relative_fileloc == expected_relative
    def test__processor_dags_folder(self, session):
        """Only populated after deserializtion"""
        dag = DAG(dag_id="test")
        dag.fileloc = "/abc/test.py"
        assert dag._processor_dags_folder is None
        sdm = SerializedDagModel(dag)
        assert sdm.dag._processor_dags_folder == settings.DAGS_FOLDER
    @pytest.mark.need_serialized_dag
    def test_dags_needing_dagruns_dataset_triggered_dag_info_queued_times(self, session, dag_maker):