### 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,
        dag_id: str | None = None,
        run_id: str | None = None,
        queued_at: datetime | None | ArgNotSet = NOTSET,
        execution_date: datetime | None = None,
        start_date: datetime | None = None,
        external_trigger: bool | None = None,
        conf: Any | None = None,
        state: DagRunState | None = None,
        run_type: str | None = None,
        dag_hash: str | None = None,
        creating_job_id: int | None = None,
        data_interval: tuple[datetime, datetime] | None = None,
    ):
        if data_interval is None:
            
            self.data_interval_start = self.data_interval_end = None
        else:
            self.data_interval_start, self.data_interval_end = data_interval
        self.dag_id = dag_id
        self.run_id = run_id
        self.execution_date = execution_date
        self.start_date = start_date
        self.external_trigger = external_trigger
        self.conf = conf or {}
        if state is not None: