### 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)

dr.update_state()
    session.flush()
    dr = session.query(DagRun).one()
    assert dr.state == DagRunState.FAILED
@pytest.mark.parametrize(
    "input, expected",
    [
        (["s1 >> w1 >> t1"], {"w1"}),  
        (["s1 >> w1 >> t1", "s1 >> t1"], {"w1"}),  
        (["s1 >> w1"], {"w1"}),  
        (["s1 >> w1 >> t1_"], {"t1_"}),  
        (["s1 >> w1 >> t1_", "s1 >> t1_"], {"t1_"}),  
        (["s1 >> w1 >> t1_ >> w2", "s1 >> t1_"], {"w2"}),  
        (["s1 >> w1 >> t1_ >> w2", "s1 >> t1_"], {"w2"}),  
        (["t1 >> t2"], {"t2"}),  
        (["w1 >> t1_ >> t2"], {"t1_"}),  
    ],
)
def test_tis_considered_for_state(dag_maker, session, input, expected):
    """
    We use a convenience notation to wire up test scenarios:
    t<num> -- teardown task
    t<num>_ -- teardown task with on_failure_fail_dagrun = True
    s<num> -- setup task
    w<num> -- work task (a.k.a. normal task)
    In the test input, each line is a statement. We'll automatically create the tasks and wire them up
    as indicated in the test input.
    """
    @teardown
    def teardown_task():