### 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 datetime import datetime, timedelta
from pathlib import Path
from typing import TYPE_CHECKING, Collection, DefaultDict, Iterator
from sqlalchemy import and_, func, not_, or_, text
from sqlalchemy.exc import OperationalError
from sqlalchemy.orm import load_only, selectinload
from sqlalchemy.orm.session import Session, make_transient
from sqlalchemy.sql import expression
from airflow import settings
from airflow.callbacks.callback_requests import DagCallbackRequest, SlaCallbackRequest, TaskCallbackRequest
from airflow.callbacks.pipe_callback_sink import PipeCallbackSink
from airflow.configuration import conf
from airflow.exceptions import RemovedInAirflow3Warning
from airflow.executors.executor_loader import ExecutorLoader
from airflow.jobs.base_job_runner import BaseJobRunner
from airflow.jobs.job import Job, perform_heartbeat
from airflow.models.dag import DAG, DagModel
from airflow.models.dagbag import DagBag
from airflow.models.dagrun import DagRun
from airflow.models.dataset import (
    DagScheduleDatasetReference,
    DatasetDagRunQueue,
    DatasetEvent,
    DatasetModel,
    TaskOutletDatasetReference,
)
from airflow.models.serialized_dag import SerializedDagModel
from airflow.models.taskinstance import SimpleTaskInstance, TaskInstance, TaskInstanceKey
from airflow.stats import Stats
from airflow.ti_deps.dependencies_states import EXECUTION_STATES