I would like to use the popup I created in my AGOL webmap when using the Search widget. I have not been able to find any examples where I can set the popupTemplate to the same template as when you lick on a feature in the map.
If I understood you correctly, you want to search a layer in the search widget, then jump to the found feature and open its popup.
If you work in a web map, you have to make the layer searchable in the map settings. Follow these instructions: https://doc.arcgis.com/en/arcgis-online/create-maps/configure-feature-search.htm
If you work in a web app, you have to edit the settings of the search widget. Follow these instructions: https://doc.arcgis.com/en/web-appbuilder/create-apps/widget-search.htm