### 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)

tis_to_reset_or_adopt = with_row_locks(
                        query, of=TI, session=session, **skip_locked(session=session)
                    ).all()
                    to_reset = self.executor.try_adopt_task_instances(tis_to_reset_or_adopt)
                    reset_tis_message = []
                    for ti in to_reset:
                        reset_tis_message.append(repr(ti))
                        ti.state = State.NONE
                        ti.queued_by_job_id = None
                    for ti in set(tis_to_reset_or_adopt) - set(to_reset):
                        ti.queued_by_job_id = self.id
                    Stats.incr("scheduler.orphaned_tasks.cleared", len(to_reset))
                    Stats.incr("scheduler.orphaned_tasks.adopted", len(tis_to_reset_or_adopt) - len(to_reset))
                    if to_reset:
                        task_instance_str = "\n\t".join(reset_tis_message)
                        self.log.info(
                            "Reset the following %s orphaned TaskInstances:\n\t%s",
                            len(to_reset),
                            task_instance_str,
                        )
                    
                    
                    session.flush()
                except OperationalError:
                    session.rollback()
                    raise
        return len(to_reset)
    @provide_session
    def check_trigger_timeouts(self, session: Session = NEW_SESSION) -> None: