A follow up…
The zoom level for the widget is set to automatic. So I assume that the zoom level in the widget is being picked up from the source map. The zoom in the source map is being set in the map editor. You can see that it is being set correctly even when the POI has been moved. As mentioned above, it shows correctly when the map is first displayed and it is set correctly in the database. So the right zoom level is there even if the POI has been moved. But for some reason, it seems to get lost when the map is centered and when the map is used in a widget.
Setting a specific zoom level in the widget doesn’t help as the source maps that feed the widget all have different zoom levels.