### 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 SchedulerJob runs for a specific time interval and schedules the jobs
    that are ready to run. It figures out the latest runs for each
    task and sees if the dependencies for the next schedules are met.
    If so, it creates appropriate TaskInstances and sends run commands to the
    executor. It does this for each task in each DAG and repeats.
    :param subdir: directory containing Python files with Airflow DAG
        definitions, or a specific path to a file
    :param num_runs: The number of times to run the scheduling loop. If you
        have a large number of DAG files this could complete before each file
        has been parsed. -1 for unlimited times.
    :param num_times_parse_dags: The number of times to try to parse each DAG file.
        -1 for unlimited times.
    :param scheduler_idle_sleep_time: The number of seconds to wait between
        polls of running processors
    :param do_pickle: once a DAG object is obtained by executing the Python
        file, whether to serialize the DAG object to the DB
    :param log: override the default Logger
    """
    __mapper_args__ = {"polymorphic_identity": "SchedulerJob"}
    heartrate: int = conf.getint("scheduler", "SCHEDULER_HEARTBEAT_SEC")
    def __init__(