### 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)

#
#
#
from __future__ import annotations
import collections
import logging
import multiprocessing
import os
import pathlib
import random
import socket
import sys
import threading
import time
from datetime import datetime, timedelta
from logging.config import dictConfig
from tempfile import TemporaryDirectory
from textwrap import dedent
from unittest import mock
from unittest.mock import MagicMock, PropertyMock
import pytest
import time_machine
from sqlalchemy import func
from airflow.callbacks.callback_requests import CallbackRequest, DagCallbackRequest, SlaCallbackRequest
from airflow.config_templates.airflow_local_settings import DEFAULT_LOGGING_CONFIG
from airflow.configuration import conf
from airflow.dag_processing.manager import (
    DagFileProcessorAgent,
    DagFileProcessorManager,
    DagFileStat,