By default have the Full Extent button zoom to the full extent of operational layers and ignore the basemap's extent. For each map I have to go in and set a custom extent so the Full Extent button does not zoom out to show the entire world.
Then add a toggle in the Map properties to include the basemap's extent.
I think it would also be useful to add a global setting for this in the main ArcGIS Pro Options so users can choose the default behavior in all their maps.