### 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 for POST request."""
    hook = HttpAsyncHook()
    aioresponse.post(
        "http://test:8080/v1/test",
        status=200,
        payload='{"status":{"status": 200}}',
        reason="OK",
    )
    with mock.patch("airflow.hooks.base.BaseHook.get_connection", side_effect=get_airflow_connection):
        resp = await hook.run("v1/test")
        assert resp.status == 200
@pytest.mark.asyncio
async def test_async_post_request_with_error_code(aioresponse):
    """Test api call asynchronously for POST request with error."""
    hook = HttpAsyncHook()
    aioresponse.post(
        "http://test:8080/v1/test",
        status=418,
        payload='{"status":{"status": 418}}',
        reason="I am teapot",
    )
    with mock.patch("airflow.hooks.base.BaseHook.get_connection", side_effect=get_airflow_connection):
        with pytest.raises(AirflowException):
            await hook.run("v1/test")