### 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)

from airflow.dag_processing.manager import DagFileProcessorAgent
        self.log.info("Starting the scheduler")
        executor_class, _ = ExecutorLoader.import_default_executor_cls()
        
        pickle_dags = self.do_pickle and executor_class.supports_pickling
        self.log.info("Processing each file at most %s times", self.num_times_parse_dags)
        
        
        async_mode = not self.using_sqlite
        processor_timeout_seconds: int = conf.getint("core", "dag_file_processor_timeout")
        processor_timeout = timedelta(seconds=processor_timeout_seconds)
        if not self._standalone_dag_processor:
            self.processor_agent = DagFileProcessorAgent(
                dag_directory=Path(self.subdir),
                max_runs=self.num_times_parse_dags,
                processor_timeout=processor_timeout,
                dag_ids=[],
                pickle_dags=pickle_dags,
                async_mode=async_mode,
            )
        try:
            self.job.executor.job_id = self.job.id
            if self.processor_agent:
                self.log.debug("Using PipeCallbackSink as callback sink.")
                self.job.executor.callback_sink = PipeCallbackSink(
                    get_sink_pipe=self.processor_agent.get_callbacks_pipe
                )
            else:
                from airflow.callbacks.database_callback_sink import DatabaseCallbackSink
                self.log.debug("Using DatabaseCallbackSink as callback sink.")