### 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)

self,
        schedulable_tis: Iterable[TI],
        session: Session = NEW_SESSION,
        max_tis_per_query: int | None = None,
    ) -> int:
        """
        Set the given task instances in to the scheduled state.
        Each element of ``schedulable_tis`` should have its ``task`` attribute already set.
        Any EmptyOperator without callbacks or outlets is instead set straight to the success state.
        All the TIs should belong to this DagRun, but this code is in the hot-path, this is not checked -- it
        is the caller's responsibility to call this function only with TIs from a single dag run.
        """
        
        
        dummy_ti_ids = []
        schedulable_ti_ids = []
        for ti in schedulable_tis:
            if (
                ti.task.inherits_from_empty_operator
                and not ti.task.on_execute_callback
                and not ti.task.on_success_callback
                and not ti.task.outlets
            ):
                dummy_ti_ids.append((ti.task_id, ti.map_index))
            else: