Have you eaten supper yet?
So, you would know right away what was served for dinner? My guess here that the word zuppa is used at home and cena at home and restaurants. Btw Japanese eat soup for breakfast. Miso soup. Speaking of soups.
This seems simply wrong. There is no definition offered in either my bilingual dictionary or Treccani that supports the use of “la zuppa” as supper. “Inzuppare” means to dunk food in broth (or a biscotti in vin santo), but no “supper” per se.
Mystery…
I found in ReversoContext under zuppa the words in this order: soup, chowder, stew, supper. In Reverso translation under zuppa : soup, chowder, zuppa. When you look at the bottom under zuppa you will find a charming sentence with no less charming translation. Zuppa, zuppa, zuppa, zuppa and translation: supper, supper, supper, supper. If all of it is true, I am very hungry now typing this.
Thank you! Perhaps it is like the English expression “soup’s on!” then - to mean the meal is ready.
I guess I need to use “ReversoContext” more too - that’s a good resource I forget about.
Exactly, I could imagine a similarly confusing translation from Yorkshire English, where “dinner” means “pranzo”, but especially, where “tea” means “cena” 
And then there are School Dinners…
In passing, zuppo means drenched or soaked and (at least according to Clozemaster) inzuppato can also be used when describing someone who has got caught in the rain. I like that. “I just got ensouped!”