### 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)

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) -> bool:
        """
        Only run DagRun.verify integrity if Serialized DAG has changed since it is slow.
        Return True if we determine that DAG still exists.
        """
        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 True
        dag_run.dag_hash = latest_version
        
        dag_run.dag = self.dagbag.get_dag(dag_id=dag_run.dag_id, session=session)
        if not dag_run.dag:
            return False
        
        dag_run.verify_integrity(session=session)
        return True
    def _send_dag_callbacks_to_processor(self, dag: DAG, callback: DagCallbackRequest | None = None) -> None: