### Apache Airflow version

2.4.2

### What happened

Hi all,

I would like to update the scheduler_job.py script by removing the unused attribute -> `self.using_mysql`.

I understand that `self.using_sqlite` attribute is used to define the variable `async_mode` in scheduler_job.py code, but noticed that `self.using_mysql` is not used.

You can check the code from [scheduler_job.py](https://github.com/apache/airflow/blob/main/airflow/jobs/scheduler_job.py),
```python
def __init__(...):
    # Check what SQL backend we use
    sql_conn: str = conf.get_mandatory_value('database', 'sql_alchemy_conn').lower()
    self.using_sqlite = sql_conn.startswith('sqlite')   # <- only self.using_sqlite is used for async_mode
    self.using_mysql = sql_conn.startswith('mysql')

...

def _execute(self) -> None:
    ...
    async_mode = not self.using_sqlite
```

not sure it was used before, but no longer used for the current scheduler.

If it's not the major change, would you mind me to remove it from the script?

Thanks in advance!

### What you think should happen instead

_No response_

### How to reproduce

_No response_

### Operating System

-

### Versions of Apache Airflow Providers

_No response_

### Deployment

Other

### Deployment details

_No response_

### Anything else

_No response_

### Are you willing to submit PR?

- [X] 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 airflow.models.dag import DAG, DagModel
from airflow.models.dagbag import DagBag
from airflow.models.dagrun import DagRun
from airflow.models.dataset import DagScheduleDatasetReference, DatasetDagRunQueue, DatasetEvent
from airflow.models.serialized_dag import SerializedDagModel
from airflow.models.taskinstance import SimpleTaskInstance, TaskInstance, TaskInstanceKey
from airflow.stats import Stats
from airflow.ti_deps.dependencies_states import EXECUTION_STATES
from airflow.timetables.simple import DatasetTriggeredTimetable
from airflow.utils import timezone
from airflow.utils.event_scheduler import EventScheduler
from airflow.utils.retries import MAX_DB_RETRIES, retry_db_transaction, run_with_db_retries
from airflow.utils.session import NEW_SESSION, create_session, provide_session
from airflow.utils.sqlalchemy import (
    CommitProhibitorGuard,
    is_lock_not_available_error,
    prohibit_commit,
    skip_locked,
    tuple_in_condition,
    with_row_locks,
)
from airflow.utils.state import DagRunState, State, TaskInstanceState
from airflow.utils.types import DagRunType
if TYPE_CHECKING:
    from types import FrameType
    from airflow.dag_processing.manager import DagFileProcessorAgent
TI = TaskInstance
DR = DagRun
DM = DagModel
def _is_parent_process() -> bool: