### 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)

execution_date=execution_date,
            data_interval=data_interval,
            start_date=now,
            state=state,
            external_trigger=False,
        )
        if task_states is not None:
            for task_id, task_state in task_states.items():
                ti = dag_run.get_task_instance(task_id)
                ti.set_state(task_state, session)
            session.flush()
        return dag_run
    @pytest.mark.parametrize("state", [DagRunState.QUEUED, DagRunState.RUNNING])
    def test_clear_task_instances_for_backfill_unfinished_dagrun(self, state, session):
        now = timezone.utcnow()
        dag_id = "test_clear_task_instances_for_backfill_dagrun"
        dag = DAG(dag_id=dag_id, start_date=now)
        dag_run = self.create_dag_run(dag, execution_date=now, is_backfill=True, state=state, session=session)
        task0 = EmptyOperator(task_id="backfill_task_0", owner="test", dag=dag)
        ti0 = TI(task=task0, run_id=dag_run.run_id)
        ti0.run()
        qry = session.query(TI).filter(TI.dag_id == dag.dag_id).all()
        clear_task_instances(qry, session)
        session.commit()
        ti0.refresh_from_db()
        dr0 = session.query(DagRun).filter(DagRun.dag_id == dag_id, DagRun.execution_date == now).first()
        assert dr0.state == state
        assert dr0.clear_number < 1
    @pytest.mark.parametrize("state", [DagRunState.SUCCESS, DagRunState.FAILED])
    def test_clear_task_instances_for_backfill_finished_dagrun(self, state, session):