### Body

The hook uses `_headers`:

https://github.com/apache/airflow/blob/9276310a43d17a9e9e38c2cb83686a15656896b2/airflow/providers/http/hooks/http.py#L340-L341

but passes `headers` to the async function

https://github.com/apache/airflow/blob/9276310a43d17a9e9e38c2cb83686a15656896b2/airflow/providers/http/hooks/http.py#L368-L375

The task:

`headers=headers` needs to be `headers=_headers`

https://github.com/apache/airflow/blob/9276310a43d17a9e9e38c2cb83686a15656896b2/airflow/providers/http/hooks/http.py#L372

There was attempt to address it in https://github.com/apache/airflow/pull/31010 but the PR become stale as no response from the author.

### Committer

- [X] I acknowledge that I am a maintainer/committer of the Apache Airflow project.
"""Test api call asynchronously with retryable error."""
    caplog.set_level(logging.WARNING, logger="airflow.providers.http.hooks.http")
    hook = HttpAsyncHook(method="GET")
    aioresponse.get("http://httpbin.org/non_existent_endpoint", status=500, repeat=True)
    with pytest.raises(AirflowException) as exc, mock.patch.dict(
        "os.environ",
        AIRFLOW_CONN_HTTP_DEFAULT="http://httpbin.org/",
    ):
        await hook.run(endpoint="non_existent_endpoint")
    assert str(exc.value) == "500:Internal Server Error"
    assert "[Try 3 of 3] Request to http://httpbin.org/non_existent_endpoint failed" in caplog.text
@pytest.mark.asyncio
async def test_do_api_call_async_unknown_method():
    """Test api call asynchronously for unknown method."""
    hook = HttpAsyncHook(method="NOPE")
    json = {
        "existing_cluster_id": "xxxx-xxxxxx-xxxxxx",
    }
    with pytest.raises(AirflowException) as exc:
        await hook.run(endpoint="non_existent_endpoint", data=json)
    assert str(exc.value) == "Unexpected HTTP Method: NOPE"
@pytest.mark.asyncio
async def test_async_post_request(aioresponse):