### Apache Airflow version

Other Airflow 2 version (please specify below)

### What happened

Greetings!
Recently I’ve faced a problem. It seems that assigning object, which can’t be serialized to JSON, to the dag_run.conf dict cause critical errors with UI.
After executing code example in "How to reproduce": 
Grid representation of the DAG breaks with following result:
<img width="800" alt="Pasted Graphic" src="https://github.com/apache/airflow/assets/79107237/872ccde5-500f-4484-a36c-dce6b7112286">
Browse -> DAG Runs also becomes unavailable.
<img width="800" alt="Pasted Graphic 1" src="https://github.com/apache/airflow/assets/79107237/b4e3df0c-5324-41dd-96f3-032e706ab7a9">
Dag itself continues to work correctly, this affects only UI graph and dagrun/list/
I suggest to use custom dictionary with restriction on setting non json values.

### What you think should happen instead

Raise an error

### How to reproduce

Execute following task. 
Composer 2 version 2.4.2
Airflow version 2.5.3
```
@task 
def test_task(**context):
    context['dag_run'].conf["test"] = np.int64(1234)
```

### Operating System

Ubuntu 20.04.6 LTS

### Versions of Apache Airflow Providers

_No response_

### Deployment

Google Cloud Composer

### 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)

)
        runs = DagRun.next_dagruns_to_examine(state, session).all()
        assert runs == [dr]
        orm_dag.is_paused = True
        session.flush()
        runs = DagRun.next_dagruns_to_examine(state, session).all()
        assert runs == []
    @mock.patch.object(Stats, "timing")
    def test_no_scheduling_delay_for_nonscheduled_runs(self, stats_mock, session):
        """
        Tests that dag scheduling delay stat is not called if the dagrun is not a scheduled run.
        This case is manual run. Simple test for coherence check.
        """
        dag = DAG(dag_id="test_dagrun_stats", start_date=DEFAULT_DATE)
        dag_task = EmptyOperator(task_id="dummy", dag=dag)
        initial_task_states = {
            dag_task.task_id: TaskInstanceState.SUCCESS,
        }
        dag_run = self.create_dag_run(dag=dag, task_states=initial_task_states, session=session)
        dag_run.update_state()
        assert call(f"dagrun.{dag.dag_id}.first_task_scheduling_delay") not in stats_mock.mock_calls
    @pytest.mark.parametrize(
        "schedule_interval, expected",
        [
            ("*/5 * * * *", True),
            (None, False),
            ("@once", False),
        ],
    )
    def test_emit_scheduling_delay(self, session, schedule_interval, expected):