### 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)

session.add(dr)
        session.commit()
        assert dr.end_date is None
        dr.set_state(DagRunState.SUCCESS)
        session.merge(dr)
        session.commit()
        dr_database = session.query(DagRun).filter(DagRun.run_id == "test_dagrun_set_state_end_date").one()
        assert dr_database.end_date is not None
        assert dr.end_date == dr_database.end_date
        dr.set_state(DagRunState.RUNNING)
        session.merge(dr)
        session.commit()
        dr_database = session.query(DagRun).filter(DagRun.run_id == "test_dagrun_set_state_end_date").one()
        assert dr_database.end_date is None
        dr.set_state(DagRunState.FAILED)
        session.merge(dr)
        session.commit()
        dr_database = session.query(DagRun).filter(DagRun.run_id == "test_dagrun_set_state_end_date").one()
        assert dr_database.end_date is not None
        assert dr.end_date == dr_database.end_date
    def test_dagrun_update_state_end_date(self, session):
        dag = DAG(
            "test_dagrun_update_state_end_date", start_date=DEFAULT_DATE, default_args={"owner": "owner1"}
        )
        
        with dag:
            op1 = EmptyOperator(task_id="A")
            op2 = EmptyOperator(task_id="B")