### 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)

return callback_to_execute
        if dag_run.execution_date > timezone.utcnow() and not dag.allow_future_exec_dates:
            self.log.error("Execution date is in future: %s", dag_run.execution_date)
            return callback
        self._verify_integrity_if_dag_changed(dag_run=dag_run, session=session)
        
        schedulable_tis, callback_to_run = dag_run.update_state(session=session, execute_callbacks=False)
        if dag_run.state in State.finished:
            active_runs = dag.get_num_active_runs(only_running=False, session=session)
            
            if self._should_update_dag_next_dagruns(dag, dag_model, active_runs):
                dag_model.calculate_dagrun_date_fields(dag, dag.get_run_data_interval(dag_run))
        
        
        
        
        dag_run.schedule_tis(schedulable_tis, session)
        return callback_to_run
    def _verify_integrity_if_dag_changed(self, dag_run: DagRun, session: Session) -> None:
        """Only run DagRun.verify integrity if Serialized DAG has changed since it is slow"""
        latest_version = SerializedDagModel.get_latest_version_hash(dag_run.dag_id, session=session)
        if dag_run.dag_hash == latest_version:
            self.log.debug("DAG %s not changed structure, skipping dagrun.verify_integrity", dag_run.dag_id)
            return
        dag_run.dag_hash = latest_version
        
        dag_run.dag = self.dagbag.get_dag(dag_id=dag_run.dag_id, session=session)
        
        dag_run.verify_integrity(session=session)
    def _send_dag_callbacks_to_processor(self, dag: DAG, callback: DagCallbackRequest | None = None) -> None: