### 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)

callback_tuples = self._schedule_all_dag_runs(guard, dag_runs, session)
        
        for dag_run, callback_to_run in callback_tuples:
            dag = self.dagbag.get_dag(dag_run.dag_id, session=session)
            if not dag:
                self.log.error("DAG '%s' not found in serialized_dag table", dag_run.dag_id)
                continue
            
            
            self._send_dag_callbacks_to_processor(dag, callback_to_run)
        with prohibit_commit(session) as guard:
            
            session.expunge_all()
            
            if self.job.executor.slots_available <= 0:
                
                self.log.debug("Executor full, skipping critical section")
                num_queued_tis = 0
            else:
                try:
                    timer = Stats.timer("scheduler.critical_section_duration")
                    timer.start()
                    
                    num_queued_tis = self._critical_section_enqueue_task_instances(session=session)
                    
                    
                    timer.stop(send=True)
                except OperationalError as e:
                    timer.stop(send=False)