Thanks @JimBarry this worked for me. I included a general example of what I did in case anybody is interested. The documentation for the assign_to_items() method shows the function call with a JSON array of item objects - 3 in that example. My array is an array of 1, but obviously more efficient to update or assign categories to multiple items at once. I will pursue this from a Pandas Dataframe. I will update or post again once I get to that point. BOTTOM LINE: assigning categories to groups is very doable. FYI - a nice article on the Category Gallery Instant App posted by ESRI's own @BernSzukalski that inspired me to create Group Categories for organizational purposes specifically for the Category Gallery.
from arcgis.gis import GIS
from arcgis.gis import Group
my_gis = GIS(username = u_name, password = p_word)
# group_id is a string of numbers of text FYI (for those unaware)
group_id = <find itemid for group, i.e. dc74b222222269e9a54f81afaed0066>
# get group
target_group = Group(my_gis, group_id)
# search items (adjust this to find your items)
items = target_group.content.search(query = "owner: <my_agol_username> AND group:{}".format(group_id),item_type="Feature Service", max_items = 125)
# index of 0 is an an example. Find index for target_item
item = items[0]
# you need item_id # as with group_id above
item_id = item.item_id
# category = transportation in this example
json_temp = [{item_id: {"categories": ["/Categories/transportation"]}}]
target_group.categories.assign_to_items(json_temp)
@JimBarry. This worked for me.