it's not "zupa" because it's accusative case and the verb "jem" is doing something to the noun "zupa".
Its so weird for me to say "eat soup" instead of "drink soup"
In Poland when You use cutlery - You eat.
For me it's the opposite. It feels strange to say "I'm drinking soup."
There are some clear soups you can drink. They are served
in cups or mugs for that purpose: clear red borscht (barszcz
czerwony czysty), clear broth (rosół, bulion).
We have those in Russian too! Rassol'nik, cholodnyj borś, zʲelionyj borś, buľjon! Interesting!
Yum. Barszcz jest smaczne.
Smaczny. Dziękuje va-dim. :)
How would I say "I am eating tomato soup?" Is it like italian where you say tomato after soup?
Jem zupę pomidorową.
The noun precedes the adjective here, because pomidorowa is not a secondary or temporal property, but a classifier.
Is "Ja jem zupę" correct? Is it redundant?
Yes it's redundant, unless you're emphasizing ja.