### 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=session,
            )
            ti = dag_run.get_task_instance(dag_task.task_id, session)
            ti.set_state(TaskInstanceState.SUCCESS, session)
            session.flush()
            with mock.patch.object(Stats, "timing") as stats_mock:
                dag_run.update_state(session)
            metric_name = f"dagrun.{dag.dag_id}.first_task_scheduling_delay"
            if expected:
                true_delay = ti.start_date - dag_run.data_interval_end
                sched_delay_stat_call = call(metric_name, true_delay, tags=expected_stat_tags)
                sched_delay_stat_call_with_tags = call(
                    "dagrun.first_task_scheduling_delay", true_delay, tags=expected_stat_tags
                )
                assert (
                    sched_delay_stat_call in stats_mock.mock_calls
                    and sched_delay_stat_call_with_tags in stats_mock.mock_calls
                )
            else:
                
                sched_delay_stat_call = call(
                    metric_name,
                    mock.ANY,
                )
                assert sched_delay_stat_call not in stats_mock.mock_calls
        finally:
            
            session.rollback()
            session.close()
    def test_states_sets(self, session):