### 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)

tis_for_dagrun_state = self._tis_for_dagrun_state(dag=dag, tis=tis)
        
        if not unfinished.tis and any(x.state in State.failed_states for x in tis_for_dagrun_state):
            self.log.error("Marking run %s failed", self)
            self.set_state(DagRunState.FAILED)
            self.notify_dagrun_state_changed(msg="task_failure")
            if execute_callbacks:
                dag.handle_callback(self, success=False, reason="task_failure", session=session)
            elif dag.has_on_failure_callback:
                from airflow.models.dag import DagModel
                dag_model = DagModel.get_dagmodel(dag.dag_id, session)
                callback = DagCallbackRequest(
                    full_filepath=dag.fileloc,
                    dag_id=self.dag_id,
                    run_id=self.run_id,
                    is_failure_callback=True,
                    processor_subdir=None if dag_model is None else dag_model.processor_subdir,
                    msg="task_failure",
                )
        
        elif not unfinished.tis and all(x.state in State.success_states for x in tis_for_dagrun_state):
            self.log.info("Marking run %s successful", self)
            self.set_state(DagRunState.SUCCESS)
            self.notify_dagrun_state_changed(msg="success")
            if execute_callbacks:
                dag.handle_callback(self, success=True, reason="success", session=session)
            elif dag.has_on_success_callback:
                from airflow.models.dag import DagModel
                dag_model = DagModel.get_dagmodel(dag.dag_id, session)
                callback = DagCallbackRequest(