### 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)

def on_success_callable(context):
            assert context["dag_run"].dag_id == "test_dagrun_update_state_with_handle_callback_success"
        dag = DAG(
            dag_id="test_dagrun_update_state_with_handle_callback_success",
            start_date=datetime.datetime(2017, 1, 1),
            on_success_callback=on_success_callable,
        )
        DAG.bulk_write_to_db(dags=[dag], processor_subdir="/tmp/test", session=session)
        dag_task1 = EmptyOperator(task_id="test_state_succeeded1", dag=dag)
        dag_task2 = EmptyOperator(task_id="test_state_succeeded2", dag=dag)
        dag_task1.set_downstream(dag_task2)
        initial_task_states = {
            "test_state_succeeded1": TaskInstanceState.SUCCESS,
            "test_state_succeeded2": TaskInstanceState.SUCCESS,
        }
        
        dag = SerializedDAG.from_dict(SerializedDAG.to_dict(dag))
        dag_run = self.create_dag_run(dag=dag, task_states=initial_task_states, session=session)
        _, callback = dag_run.update_state(execute_callbacks=False)
        assert DagRunState.SUCCESS == dag_run.state
        
        assert callback == DagCallbackRequest(
            full_filepath=dag_run.dag.fileloc,
            dag_id="test_dagrun_update_state_with_handle_callback_success",
            run_id=dag_run.run_id,
            is_failure_callback=False,
            processor_subdir="/tmp/test",
            msg="success",
        )
    def test_dagrun_update_state_with_handle_callback_failure(self, session):