### 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)

"""
        Return the Dag associated with this DagRun.
        :return: DAG
        """
        if not self.dag:
            raise AirflowException(f"The DAG (.dag) for {self} needs to be set")
        return self.dag
    @staticmethod
    @internal_api_call
    @provide_session
    def get_previous_dagrun(
        dag_run: DagRun | DagRunPydantic, state: DagRunState | None = None, session: Session = NEW_SESSION
    ) -> DagRun | None:
        """
        Return the previous DagRun, if there is one.
        :param dag_run: the dag run
        :param session: SQLAlchemy ORM Session
        :param state: the dag run state
        """
        filters = [
            DagRun.dag_id == dag_run.dag_id,
            DagRun.execution_date < dag_run.execution_date,
        ]
        if state is not None:
            filters.append(DagRun.state == state)
        return session.scalar(select(DagRun).where(*filters).order_by(DagRun.execution_date.desc()).limit(1))
    @staticmethod
    @internal_api_call
    @provide_session
    def get_previous_scheduled_dagrun(