In Web App Builder you can successfully share a basemap from the basemap gallery via the Share Widget, as seen in our public facing application:
https://osi.maps.arcgis.com/apps/webappviewer/index.html?id=bc56a1cf08844a2aa2609aa92e89497e
We are currently rebuilding this application as an Experience Builder application and have discovered that no matter what you change the basemap to via the Basemap Gallery widget, it is not honoured via the Share Widget, however, operational layers in the Layer List are honoured.
We would like to see this Share Widget functionality migrate over from Web App Builder to Experience Builder.
