ogr2ogr won't read directory of GeoJSON into GPKG

The "directory as dataset" is a specific feature of the shapefile driver. From http://www.gdal.org/drv_shapefile.html :

Normally the OGR Shapefile driver treats a whole directory of shapefiles as a dataset, and a single shapefile within that directory as a layer. In this case the directory name should be used as the dataset name. However, it is also possible to use one of the files (.shp, .shx or .dbf) in a shapefile set as the dataset name, and then it will be treated as a dataset with one layer.

Alternative approaches would be to load each file using a loop, or to convert to shapefiles first.