### 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)

cls,
        dag_id: str,
        run_id: str,
        execution_date: datetime,
        session: Session = NEW_SESSION,
    ) -> DagRun | None:
        """
        Return an existing run for the DAG with a specific run_id or execution_date.
        *None* is returned if no such DAG run is found.
        :param dag_id: the dag_id to find duplicates for
        :param run_id: defines the run id for this dag run
        :param execution_date: the execution date
        :param session: database session
        """
        return session.scalars(
            select(cls).where(
                cls.dag_id == dag_id,
                or_(cls.run_id == run_id, cls.execution_date == execution_date),
            )
        ).one_or_none()
    @staticmethod
    def generate_run_id(run_type: DagRunType, execution_date: datetime) -> str: