### 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.
requests_mock.post(
            "http://test:8080/v1/test", status_code=200, text='{"status":{"status": 200}}', reason="OK"
        )
        with mock.patch("airflow.hooks.base.BaseHook.get_connection", side_effect=get_airflow_connection):
            resp = self.post_hook.run("v1/test")
            assert resp.status_code == 200
    def test_post_request_with_error_code(self, requests_mock):
        requests_mock.post(
            "http://test:8080/v1/test",
            status_code=418,
            text='{"status":{"status": 418}}',
            reason="I'm a teapot",
        )
        with mock.patch("airflow.hooks.base.BaseHook.get_connection", side_effect=get_airflow_connection):
            with pytest.raises(AirflowException):
                self.post_hook.run("v1/test")
    def test_post_request_do_not_raise_for_status_if_check_response_is_false(self, requests_mock):
        requests_mock.post(
            "http://test:8080/v1/test",
            status_code=418,
            text='{"status":{"status": 418}}',
            reason="I'm a teapot",
        )
        with mock.patch("airflow.hooks.base.BaseHook.get_connection", side_effect=get_airflow_connection):
            resp = self.post_hook.run("v1/test", extra_options={"check_response": False})
            assert resp.status_code == 418
    @mock.patch("airflow.providers.http.hooks.http.requests.Session")
    def test_retry_on_conn_error(self, mocked_session):