The soup has been cooked. Is it ok?
Yes, and it works.
Am I right in assuming that 'zupa została ugotowana' is more like 'the soup was being cooked'?
No, that's kinda the opposite. Your sentence is "Zupa była gotowana", so it focuses on the process, and says absolutely nothing about the result.
"Zupa została ugotowana" means that the process of cooking was succesfully finished.
I wrote "Zupa była ugotowana" and it was correct, is this now also dokonany (successfully finished?)
To rephrase the question somewhat, what difference does "był" and "została" make here and can it be used with finished and unfinished aspect?
It was correct, because in casual speech, zostać is often substituted with być.