### Description

In tasks that perform multiple requests, the log file is getting cluttered by the logging in `run`, line 129
I propose that we add a kwarg `log_request` with default value True to control this behavior

### Use case/motivation

reduce unnecessary entries in log files

### Related issues

_No response_

### Are you willing to submit a PR?

- [X] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

checking for the result
        :param session: the session to be used to execute the request
        :param prepped_request: the prepared request generated in run()
        :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
        """
        extra_options = extra_options or {}
        settings = session.merge_environment_settings(
            prepped_request.url,
            proxies=extra_options.get("proxies", {}),
            stream=extra_options.get("stream", False),
            verify=extra_options.get("verify"),
            cert=extra_options.get("cert"),
        )
        
        send_kwargs: dict[str, Any] = {
            "timeout": extra_options.get("timeout"),
            "allow_redirects": extra_options.get("allow_redirects", True),
        }
        send_kwargs.update(settings)
        try:
            response = session.send(prepped_request, **send_kwargs)
            if extra_options.get("check_response", True):
                self.check_response(response)
            return response
        except requests.exceptions.ConnectionError as ex:
            self.log.warning("%s Tenacity will retry to execute the operation", ex)
            raise ex
    def run_with_advanced_retry(self, _retry_args: dict[Any, Any], *args: Any, **kwargs: Any) -> Any: