### 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)

qry = select(cls)
        dag_ids = [dag_id] if isinstance(dag_id, str) else dag_id
        if dag_ids:
            qry = qry.where(cls.dag_id.in_(dag_ids))
        if is_container(run_id):
            qry = qry.where(cls.run_id.in_(run_id))
        elif run_id is not None:
            qry = qry.where(cls.run_id == run_id)
        if is_container(execution_date):
            qry = qry.where(cls.execution_date.in_(execution_date))
        elif execution_date is not None:
            qry = qry.where(cls.execution_date == execution_date)
        if execution_start_date and execution_end_date:
            qry = qry.where(cls.execution_date.between(execution_start_date, execution_end_date))
        elif execution_start_date:
            qry = qry.where(cls.execution_date >= execution_start_date)
        elif execution_end_date:
            qry = qry.where(cls.execution_date <= execution_end_date)
        if state:
            qry = qry.where(cls.state == state)
        if external_trigger is not None:
            qry = qry.where(cls.external_trigger == external_trigger)
        if run_type:
            qry = qry.where(cls.run_type == run_type)
        if no_backfills:
            qry = qry.where(cls.run_type != DagRunType.BACKFILL_JOB)
        return session.scalars(qry.order_by(cls.execution_date)).all()
    @classmethod
    @provide_session
    def find_duplicate(