A customer reports that the Near Me (Beta) widget doesn't work with a custom basemap. The ArcGIS Online organization has configured a custom base map as default for all of their web maps. They developed an app in ArcGIS Experience Builder and included the Near Me (Beta) widget, but the widget loads indefinitely when selecting an area or point. However, the widget works correctly if an Esri base map is selected.
After testing this issue with different custom web maps, it only occurs when the Spatial Reference of the custom web map is different from Esri basemap's spatial reference. The widget can only work with WGS84 Web Mercator Auxiliary Sphere wkid 3857 (102100) as the spatial reference; other coordinate systems will fail. It seems that proximity and distance calculations are fixed for this spatial reference.