Try using Add Spatial Join setting the Target and Join Features to the same point feature class with the Intersect match option. The Join_Count field will display the number of matches and 2 or more signals an intersect. You can then select intersecting features with a Select interactive tool and then expand the widget and select features.
In reviewing this Esri Community post here, it seems that if you use the Find Identical GP tool with the SHAPE field as the parameter and it shows it does work with a Standard license.
Ah I see. I believe at ArcGIS Pro 3.0 or 3.1, the licensing changed to include all license levels. Can you upgrade from ArcGIS Pro 2.7.1 to ArcGIS Pro 3.x?
Try using Add Spatial Join setting the Target and Join Features to the same point feature class with the Intersect match option. The Join_Count field will display the number of matches and 2 or more signals an intersect. You can then select intersecting features with a Select interactive tool and then expand the widget and select features.