From my understanding, under the hood the Extract Data option of the Analysis widget uses the same Extract Data service that you are attempting to use in the GP widget.
So are you planning to use the service endpoint on ArcGIS Online if you are not exposing your ArcGIS Enterprise endpoints?
If so, be aware that the analysis service consumes credits.
In any case, I'm not sure it is going to be a great user experience using the GP widget with the Extract Data endpoint. The tool's parameters are not very friendly to the end user.
To get what you want, you may have to create your own widget as I couldn't find anything in the community widgets:
Web AppBuilder Custom Widgets
Mark
Regards,
Mark