### Apache Airflow version

2.5.1

### What happened

I'd expect the `scheduler.tasks.running` metric to represent the number of running tasks, but it is always zero. It appears that #10956 broke this when it removed [the line that increments `num_tasks_in_executor`](https://github.com/apache/airflow/pull/10956/files#diff-bde85feb359b12bdd358aed4106ef4fccbd8fa9915e16b9abb7502912a1c1ab3L1363). Right now that variable is set to 0, never incremented, and the emitted as a gauge.

### What you think should happen instead

`scheduler.tasks.running` should either represent the number of tasks running or be removed altogether.

### How to reproduce

_No response_

### Operating System

Ubuntu 18.04

### Versions of Apache Airflow Providers

_No response_

### Deployment

Official Apache Airflow Helm Chart

### 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)

self.num_times_parse_dags = num_times_parse_dags
        if processor_poll_interval:
            
            warnings.warn(
                "The 'processor_poll_interval' parameter is deprecated. "
                "Please use 'scheduler_idle_sleep_time'.",
                RemovedInAirflow3Warning,
                stacklevel=2,
            )
            scheduler_idle_sleep_time = processor_poll_interval
        self._scheduler_idle_sleep_time = scheduler_idle_sleep_time
        
        self._zombie_threshold_secs = conf.getint("scheduler", "scheduler_zombie_task_threshold")
        self._standalone_dag_processor = conf.getboolean("scheduler", "standalone_dag_processor")
        self._dag_stale_not_seen_duration = conf.getint("scheduler", "dag_stale_not_seen_duration")
        self.do_pickle = do_pickle
        if log:
            self._log = log
        
        sql_conn: str = conf.get_mandatory_value("database", "sql_alchemy_conn").lower()
        self.using_sqlite = sql_conn.startswith("sqlite")
        
        self.processor_agent: DagFileProcessorAgent | None = None
        self.dagbag = DagBag(dag_folder=self.subdir, read_dags_from_db=True, load_op_links=False)
        self._paused_dag_without_running_dagruns: set = set()
    @provide_session
    def heartbeat_callback(self, session: Session = NEW_SESSION) -> None: