### Apache Airflow version

Other Airflow 2 version (please specify below)

### What happened

### Deployment 
* Airflow Version: 2.4.1
* Infrastructure: AWS ECS
* Number of DAG: 162
```
Version: [v2.4.1](https://pypi.python.org/pypi/apache-airflow/2.4.1)
Git Version: .release:2.4.1+7b979def75923ba28dd64e31e613043d29f34fce
```

### The issue

We have seen this issue when the Scheduler is trying to schedule **too many DAG (140+)** around the same time 

```
[2022-11-11T00:15:00.311+0000] {{dagbag.py:196}} WARNING - Serialized DAG mongodb-assistedbreakdown-jobs-processes no longer exists
[2022-11-11T00:15:00.312+0000] {{scheduler_job.py:763}} ERROR - Exception when executing SchedulerJob._run_scheduler_loop
Traceback (most recent call last):
  File "/home/airflow/.local/lib/python3.7/site-packages/airflow/jobs/scheduler_job.py", line 746, in _execute
    self._run_scheduler_loop()
  File "/home/airflow/.local/lib/python3.7/site-packages/airflow/jobs/scheduler_job.py", line 866, in _run_scheduler_loop
    num_queued_tis = self._do_scheduling(session)
  File "/home/airflow/.local/lib/python3.7/site-packages/airflow/jobs/scheduler_job.py", line 948, in _do_scheduling
    callback_to_run = self._schedule_dag_run(dag_run, session)
  File "/home/airflow/.local/lib/python3.7/site-packages/airflow/jobs/scheduler_job.py", line 1292, in _schedule_dag_run
    self._verify_integrity_if_dag_changed(dag_run=dag_run, session=session)
  File "/home/airflow/.local/lib/python3.7/site-packages/airflow/jobs/scheduler_job.py", line 1321, in _verify_integrity_if_dag_changed
    dag_run.verify_integrity(session=session)
  File "/home/airflow/.local/lib/python3.7/site-packages/airflow/utils/session.py", line 72, in wrapper
    return func(*args, **kwargs)
  File "/home/airflow/.local/lib/python3.7/site-packages/airflow/models/dagrun.py", line 874, in verify_integrity
    dag = self.get_dag()
  File "/home/airflow/.local/lib/python3.7/site-packages/airflow/models/dagrun.py", line 484, in get_dag
    raise AirflowException(f"The DAG (.dag) for {self} needs to be set")
airflow.exceptions.AirflowException: The DAG (.dag) for <DagRun mongodb-assistedbreakdown-jobs-processes @ 2022-11-10 00:10:00+00:00: scheduled__2022-11-10T00:10:00+00:00, state:running, queued_at: 2022-11-11 00:10:09.363852+00:00. externally triggered: False> needs to be set
```
Main Cause
```
raise AirflowException(f"The DAG (.dag) for {self} needs to be set")
```

[We believe this is happening here, airflow github](https://github.com/apache/airflow/blob/7b979def75923ba28dd64e31e613043d29f34fce/airflow/jobs/scheduler_job.py#L1318)


We saw a large amount of Connection hitting our airflow Database, but CPU was around 60%. Is there any workaround or configuration that can help the scheduler not crash when this happen?

### What you think should happen instead

Can the scheduler be safe, or when it come back to reschedule the dags that got stuck 

### How to reproduce

_No response_

### Operating System

Amazon Linux 2, Fargate deployment using the airflow Image

### Versions of Apache Airflow Providers

_No response_

### Deployment

Other

### Deployment details

AWS ECS Fargate

### 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)

"""
        This function is where the main scheduling decisions take places. It:
        - Creates any necessary DAG runs by examining the next_dagrun_create_after column of DagModel
          Since creating Dag Runs is a relatively time consuming process, we select only 10 dags by default
          (configurable via ``scheduler.max_dagruns_to_create_per_loop`` setting) - putting this higher will
          mean one scheduler could spend a chunk of time creating dag runs, and not ever get around to
          scheduling tasks.
        - Finds the "next n oldest" running DAG Runs to examine for scheduling (n=20 by default, configurable
          via ``scheduler.max_dagruns_per_loop_to_schedule`` config setting) and tries to progress state (TIs
          to SCHEDULED, or DagRuns to SUCCESS/FAILURE etc)
          By "next oldest", we mean hasn't been examined/scheduled in the most time.
          We don't select all dagruns at once, because the rows are selected with row locks, meaning
          that only one scheduler can "process them", even it is waiting behind other dags. Increasing this
          limit will allow more throughput for smaller DAGs but will likely slow down throughput for larger
          (>500 tasks.) DAGs
        - Then, via a Critical Section (locking the rows of the Pool model) we queue tasks, and then send them
          to the executor.
          See docs of _critical_section_enqueue_task_instances for more.
        :return: Number of TIs enqueued in this iteration
        """
        
        with prohibit_commit(session) as guard:
            if settings.USE_JOB_SCHEDULE:
                self._create_dagruns_for_dags(guard, session)
            self._start_queued_dagruns(session)
            guard.commit()
            dag_runs = self._get_next_dagruns_to_examine(DagRunState.RUNNING, session)