### 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)

"""
        Verify the DagRun by checking for removed tasks or tasks that are not in the database yet.
        It will set state to removed or add the task if required.
        :missing_indexes: A dictionary of task vs indexes that are missing.
        :param session: Sqlalchemy ORM Session
        """
        from airflow.settings import task_instance_mutation_hook
        
        
        hook_is_noop: Literal[True, False] = getattr(task_instance_mutation_hook, "is_noop", False)
        dag = self.get_dag()
        task_ids = self._check_for_removed_or_restored_tasks(
            dag, task_instance_mutation_hook, session=session
        )
        def task_filter(task: Operator) -> bool:
            return task.task_id not in task_ids and (
                self.is_backfill
                or task.start_date <= self.execution_date
                and (task.end_date is None or self.execution_date <= task.end_date)
            )
        created_counts: dict[str, int] = defaultdict(int)
        task_creator = self._get_task_creator(created_counts, task_instance_mutation_hook, hook_is_noop)
        
        tasks_to_create = (task for task in dag.task_dict.values() if task_filter(task))
        tis_to_create = self._create_tasks(tasks_to_create, task_creator, session=session)
        self._create_task_instances(self.dag_id, tis_to_create, created_counts, hook_is_noop, session=session)
    def _check_for_removed_or_restored_tasks(