### 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)

"idx_dag_run_queued_dags",
            "state",
            "dag_id",
            postgresql_where=text("state='queued'"),
            mssql_where=text("state='queued'"),
            sqlite_where=text("state='queued'"),
        ),
    )
    task_instances = relationship(
        TI, back_populates="dag_run", cascade="save-update, merge, delete, delete-orphan"
    )
    dag_model = relationship(
        "DagModel",
        primaryjoin="foreign(DagRun.dag_id) == DagModel.dag_id",
        uselist=False,
        viewonly=True,
    )
    dag_run_note = relationship(
        "DagRunNote",
        back_populates="dag_run",
        uselist=False,
        cascade="all, delete, delete-orphan",
    )
    note = association_proxy("dag_run_note", "content", creator=_creator_note)
    DEFAULT_DAGRUNS_TO_EXAMINE = airflow_conf.getint(
        "scheduler",
        "max_dagruns_per_loop_to_schedule",
        fallback=20,
    )
    def __init__(