there is one reporting attribute called classifications type (the main category in classifications):
Attached .skc for NAHB cost codes as a zip, unzip it and import through Model Info > Classifications
NAHB cost codes.skc.zip (4,1 KB)
BTW, all custom attributes that are created by an extension (Dictionaries) do end up in the data table manager of the 3D Viewer (yeah…Trimble Connect):
and custom dictionaries that you manually enter through Attribute inspector: