### 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.
self,
        endpoint: str | None = None,
        data: dict[str, Any] | str | None = None,
        headers: dict[str, Any] | None = None,
        extra_options: dict[str, Any] | None = None,
        **request_kwargs: Any,
    ) -> Any:
        r"""Perform the request.
        :param endpoint: the endpoint to be called i.e. resource/v1/query?
        :param data: payload to be uploaded or request parameters
        :param headers: additional headers to be passed through as a dictionary
        :param extra_options: additional options to be used when executing the request
            i.e. {'check_response': False} to avoid checking raising exceptions on non
            2XX or 3XX status codes
        :param request_kwargs: Additional kwargs to pass when creating a request.
            For example, ``run(json=obj)`` is passed as ``requests.Request(json=obj)``
        """
        extra_options = extra_options or {}
        session = self.get_conn(headers)
        url = self.url_from_endpoint(endpoint)
        if self.tcp_keep_alive:
            keep_alive_adapter = TCPKeepAliveAdapter(
                idle=self.keep_alive_idle, count=self.keep_alive_count, interval=self.keep_alive_interval
            )
            session.mount(url, keep_alive_adapter)