Oh Jesus, workaround == life saver!! Found out, it's already enough if you simply select the published field of the parent paragraph bundle to be translatable under /admin/config/regional/content-language.
Shit, the "workaround" introduces another major downer: The first time after the workaround you add a new paragraph item in the original language all original language paragraph items get synced to the translation language again, replacing the translations. After that it's fine. It's just the first time this happens.