i have never used any kind of meat or meat broth or sugar or cabbage,
and i usually blend the soup to make it smoothe.

i never thought of adding thickener such as corn starch,
or horseradish, but have used golden beets, and alway
a "dollop" of sour cream...

i usually boil beets, onions and garlic (and maybe a carrot or two)
til soft, then whirl in a blender, and
eat. I see bottles of borscht in the store
in the kosher shelves at certain time of year.

beets or beet juice is also great in pickled eggs...