### 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.
with mock.patch("airflow.hooks.base.BaseHook.get_connection", side_effect=get_airflow_connection):
            auth.return_value = None
            auth_with_args = functools.partial(AuthBase, "test_arg")
            hook = HttpHook("GET", "http_default", auth_with_args)
            hook.get_conn()
            auth.assert_called_once_with("test_arg")
    @mock.patch("requests.auth.HTTPBasicAuth.__init__")
    def test_login_password_basic_auth_initialized(self, auth):
        with mock.patch(
            "airflow.hooks.base.BaseHook.get_connection",
            side_effect=get_airflow_connection_with_login_and_password,
        ):
            auth.return_value = None
            hook = HttpHook("GET", "http_default", HTTPBasicAuth)
            hook.get_conn()
            auth.assert_called_once_with("username", "pass")
    @mock.patch("requests.auth.HTTPBasicAuth.__init__")
    def test_default_auth_not_initialized(self, auth):
        with mock.patch("airflow.hooks.base.BaseHook.get_connection", side_effect=get_airflow_connection):
            auth.return_value = None
            hook = HttpHook("GET", "http_default")
            hook.get_conn()
            auth.assert_not_called()
class TestKeepAlive: