### 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)

def mutate_task_instance(task_instance):
            if task_instance.queue == "queue1":
                task_instance.queue = "queue2"
            else:
                task_instance.queue = "queue1"
        mock_hook.side_effect = mutate_task_instance
        dag = DAG("test_task_instance_mutation_hook", start_date=DEFAULT_DATE)
        dag.add_task(EmptyOperator(task_id="task_to_mutate", owner="test", queue="queue1"))
        dagrun = self.create_dag_run(dag, session=session)
        task = dagrun.get_task_instances()[0]
        task.state = state
        session.merge(task)
        session.commit()
        assert task.queue == "queue2"
        dagrun.verify_integrity()
        task = dagrun.get_task_instances()[0]
        assert task.queue == "queue1"
    @pytest.mark.parametrize(
        "prev_ti_state, is_ti_success",
        [
            (TaskInstanceState.SUCCESS, True),
            (TaskInstanceState.SKIPPED, True),
            (TaskInstanceState.RUNNING, False),
            (TaskInstanceState.FAILED, False),
            (None, False),
        ],
    )
    def test_depends_on_past(self, session, prev_ti_state, is_ti_success):