### 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)

ForeignKey("log_template.id", name="task_instance_log_template_id_fkey", ondelete="NO ACTION"),
        default=select(func.max(LogTemplate.__table__.c.id)),
    )
    updated_at = Column(UtcDateTime, default=timezone.utcnow, onupdate=timezone.utcnow)
    
    
    
    clear_number = Column(Integer, default=0, nullable=False)
    
    if not TYPE_CHECKING and "BUILDING_AIRFLOW_DOCS" in os.environ:
        dag: DAG | None
    else:
        dag: DAG | None = None
    __table_args__ = (
        Index("dag_id_state", dag_id, _state),
        UniqueConstraint("dag_id", "execution_date", name="dag_run_dag_id_execution_date_key"),
        UniqueConstraint("dag_id", "run_id", name="dag_run_dag_id_run_id_key"),
        Index("idx_last_scheduling_decision", last_scheduling_decision),
        Index("idx_dag_run_dag_id", dag_id),
        Index(
            "idx_dag_run_running_dags",
            "state",
            "dag_id",
            postgresql_where=text("state='running'"),
            mssql_where=text("state='running'"),
            sqlite_where=text("state='running'"),
        ),
        
        
        Index(