### 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)

select(cls)
            .with_hint(cls, "USE INDEX (idx_dag_run_running_dags)", dialect_name="mysql")
            .where(cls.state == state, cls.run_type != DagRunType.BACKFILL_JOB)
            .join(DagModel, DagModel.dag_id == cls.dag_id)
            .where(DagModel.is_paused == false(), DagModel.is_active == true())
        )
        if state == DagRunState.QUEUED:
            
            
            running_drs = (
                select(DagRun.dag_id, func.count(DagRun.state).label("num_running"))
                .where(DagRun.state == DagRunState.RUNNING)
                .group_by(DagRun.dag_id)
                .subquery()
            )
            query = query.outerjoin(running_drs, running_drs.c.dag_id == DagRun.dag_id).where(
                func.coalesce(running_drs.c.num_running, 0) < DagModel.max_active_runs
            )
        query = query.order_by(
            nulls_first(cls.last_scheduling_decision, session=session),
            cls.execution_date,
        )
        if not settings.ALLOW_FUTURE_EXEC_DATES:
            query = query.where(DagRun.execution_date <= func.now())
        return session.scalars(
            with_row_locks(query.limit(max_number), of=cls, session=session, **skip_locked(session=session))
        )
    @classmethod
    @provide_session
    def find(