### 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)

now = timezone.utcnow()
        dag_id = "test_dagrun_find_duplicate"
        dag_run = DagRun(
            dag_id=dag_id,
            run_id=dag_id,
            run_type=DagRunType.MANUAL,
            execution_date=now,
            start_date=now,
            state=DagRunState.RUNNING,
            external_trigger=True,
        )
        session.add(dag_run)
        session.commit()
        assert DagRun.find_duplicate(dag_id=dag_id, run_id=dag_id, execution_date=now) is not None
        assert DagRun.find_duplicate(dag_id=dag_id, run_id=dag_id, execution_date=None) is not None
        assert DagRun.find_duplicate(dag_id=dag_id, run_id=None, execution_date=now) is not None
        assert DagRun.find_duplicate(dag_id=dag_id, run_id=None, execution_date=None) is None
    def test_dagrun_success_when_all_skipped(self, session):
        """
        Tests that a DAG run succeeds when all tasks are skipped
        """
        dag = DAG(dag_id="test_dagrun_success_when_all_skipped", start_date=timezone.datetime(2017, 1, 1))
        dag_task1 = ShortCircuitOperator(
            task_id="test_short_circuit_false", dag=dag, python_callable=lambda: False
        )
        dag_task2 = EmptyOperator(task_id="test_state_skipped1", dag=dag)
        dag_task3 = EmptyOperator(task_id="test_state_skipped2", dag=dag)
        dag_task1.set_downstream(dag_task2)