### 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)

with conf_vars({("core", "load_examples"): "false"}):
        with env_vars({"AIRFLOW__CORE__LOAD_EXAMPLES": "false"}):
            yield
@pytest.fixture(scope="module")
def dagbag():
    from airflow.models.dagbag import DagBag
    
    non_serialized_dagbag = DagBag(read_dags_from_db=False, include_examples=False)
    non_serialized_dagbag.sync_to_db()
    return DagBag(read_dags_from_db=True)
@pytest.fixture
def load_examples():
    with conf_vars({("core", "load_examples"): "True"}):
        yield
@pytest.mark.usefixtures("disable_load_example")
@pytest.mark.need_serialized_dag
class TestSchedulerJob:
    @staticmethod
    def clean_db():
        clear_db_runs()
        clear_db_pools()
        clear_db_dags()
        clear_db_sla_miss()
        clear_db_import_errors()
        clear_db_jobs()
        clear_db_datasets()
        
        
    @pytest.fixture(autouse=True)
    def per_test(self) -> Generator: