### 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)

"""
        Enqueues TaskInstances for execution.
        There are three steps:
        1. Pick TIs by priority with the constraint that they are in the expected states
        and that we do exceed max_active_runs or pool limits.
        2. Change the state for the TIs above atomically.
        3. Enqueue the TIs in the executor.
        HA note: This function is a "critical section" meaning that only a single executor process can execute
        this function at the same time. This is achieved by doing ``SELECT ... from pool FOR UPDATE``. For DBs
        that support NOWAIT, a "blocked" scheduler will skip this and continue on with other tasks (creating
        new DAG runs, progressing TIs from None to SCHEDULED etc.); DBs that don't support this (such as
        MariaDB or MySQL 5.x) the other schedulers will wait for the lock before continuing.
        :param session:
        :return: Number of task instance with state changed.
        """
        if self.max_tis_per_query == 0:
            max_tis = self.executor.slots_available
        else:
            max_tis = min(self.max_tis_per_query, self.executor.slots_available)
        queued_tis = self._executable_task_instances_to_queued(max_tis, session=session)
        self._enqueue_task_instances_with_queued_state(queued_tis, session=session)
        return len(queued_tis)
    def _process_executor_events(self, session: Session) -> int: