At present, it is not possible to automatically ingest attribute tables from GeoPackages. GeoPackages are an increasingly popular open-source geospatial format that have several advantages over shapefiles, including using a singular file and the ability to have long, self-explanatory, attribute names.
It would be helpful to build support to automatically ingest GeoPackage attribute tables similarly to how CSV and shapefile attribute tables are ingested by browsing to the dataset. Thank you for creating such a helpful tool!