### 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 logging
import os
import struct
from datetime import datetime
from typing import Collection, Iterable
from sqlalchemy import BigInteger, Column, String, Text, delete, select
from sqlalchemy.dialects.mysql import MEDIUMTEXT
from sqlalchemy.orm import Session
from sqlalchemy.sql.expression import literal
from airflow.exceptions import AirflowException, DagCodeNotFound
from airflow.models.base import Base
from airflow.utils import timezone
from airflow.utils.file import correct_maybe_zipped, open_maybe_zipped
from airflow.utils.session import NEW_SESSION, provide_session
from airflow.utils.sqlalchemy import UtcDateTime
log = logging.getLogger(__name__)
class DagCode(Base):