### 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)

"""
        Tests that dag scheduling delay stat is set properly once running scheduled dag.
        dag_run.update_state() invokes the _emit_true_scheduling_delay_stats_for_finished_state method.
        """
        dag = DAG(dag_id="test_emit_dag_stats", start_date=DEFAULT_DATE, schedule=schedule_interval)
        dag_task = EmptyOperator(task_id="dummy", dag=dag, owner="airflow")
        expected_stat_tags = {"dag_id": f"{dag.dag_id}", "run_type": DagRunType.SCHEDULED}
        try:
            info = dag.next_dagrun_info(None)
            orm_dag_kwargs = {"dag_id": dag.dag_id, "has_task_concurrency_limits": False, "is_active": True}
            if info is not None:
                orm_dag_kwargs.update(
                    {
                        "next_dagrun": info.logical_date,
                        "next_dagrun_data_interval": info.data_interval,
                        "next_dagrun_create_after": info.run_after,
                    },
                )
            orm_dag = DagModel(**orm_dag_kwargs)
            session.add(orm_dag)
            session.flush()
            dag_run = dag.create_dagrun(
                run_type=DagRunType.SCHEDULED,
                state=DagRunState.SUCCESS,
                execution_date=dag.start_date,
                data_interval=dag.infer_automated_data_interval(dag.start_date),
                start_date=dag.start_date,