Polish nouns have different grammatical forms (endings) depending
on their grammatical gender (masculine, feminine, or neuter), the verb
they are associated with (cases) and the number (singular or plural).
The noun "zupa" ends with an "a", so it is a feminine noun.
It is (what? - Nominative) - To jest (kto? co? - Mianownik) zupa
The verb "mieć" requires the noun in Accusative. It changes the ending
of all feminine nouns (zupa, kobieta, książka, kanapka) from "a" into "ę":
to have (what? - Accusative) - mieć (kogo? co? - Biernik)
I have (what?) soup - Mam (kogo? co?) kobietę/zupę/kanapkę/książkę
You have (what?) soup - Masz/Macie (kogo? co?) kobietę/zupę/kanapkę
The term "inanimate" refers to masculine inanimate nouns. They look the same in Nominative and in Accusative, so in that sense they do not change:
It is (what? - Nominative) dinner - To jest (kto? co? - Mianownik) obiad
You have (what? - Accusative) dinner - Masz/Macie (co? - Biernik) obiad
All Polish nouns generally change (decline). But there are some exceptions, some nouns don't decline at all, e.g. salami, kiwi, emu. They are usually loanwords. Moreover "zupa" is a feminine noun. Feminine nouns always have different forms for accusative case. But thid rule is true for masculine inanimate nous, e.g. "komputer", "stół"
Not sure why, but I imagine going up to someone with soup in a restaurant in Poland and saying "masz zupę" out of context. And then the person says something along the lines of "yes, brilliant observation" in the most sarcastic way possible. I wouldn't ever do that, nor do I plan on going to Poland, but this is what always plays in my head during these questions...
Edit: I want to go to Poland now, but I'll never be able to afford it :'>
Word-final -ą should be pronounced as a "nasal o" (similar to french "en"), but some speakers denazalise it to [oł], some even to [om]. Pronouncing it as [a] would be wrong, though.
However, word final -ę can be pronounced as a plain [e] and that would be correct. Many speakers retain a slight nasality and sometimes you can even hear a full-blown nasal sound, which is a historic pronunciation and considered hypercorrect nowadays.