### 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)

session.add(tr)
    session.add(TaskFail(ti))
    XCom.set(key="test", value="value", task_id=ti.task_id, dag_id=dag.dag_id, run_id=ti.run_id)
    session.commit()
    for table in [TaskFail, TaskInstanceNote, TaskReschedule, XCom]:
        assert session.query(table).count() == 1
    dr1.task_instance_scheduling_decisions(session)
    for table in [TaskFail, TaskInstanceNote, TaskReschedule, XCom]:
        assert session.query(table).count() == 0
def test_dagrun_with_note(dag_maker, session):
    with dag_maker():
        @task
        def the_task():
            print("Hi")
        the_task()
    dr: DagRun = dag_maker.create_dagrun()
    dr.note = "dag run with note"
    session.add(dr)
    session.commit()
    dr_note = session.query(DagRunNote).filter(DagRunNote.dag_run_id == dr.id).one()
    assert dr_note.content == "dag run with note"
    session.delete(dr)
    session.commit()
    assert session.query(DagRun).filter(DagRun.id == dr.id).one_or_none() is None
    assert session.query(DagRunNote).filter(DagRunNote.dag_run_id == dr.id).one_or_none() is None
@pytest.mark.parametrize(
    "dag_run_state, on_failure_fail_dagrun", [[DagRunState.SUCCESS, False], [DagRunState.FAILED, True]]
)
def test_teardown_failure_behaviour_on_dagrun(dag_maker, session, dag_run_state, on_failure_fail_dagrun):