You have a "allgemeines Persönlichkeitsrecht" (general personal rights?) that prevents other people from publishing information that's supposed to be private.
Here's a case where someone published a facebook dm for example:
This scenario however is "I take my personal data an run it through tools to make my life easier" (heck, even backup could fit the bill here). If I'm allowed to do that... am I allowed to do that only with tools that are perfectly secure? Can I send data to the cloud? (subcases: I own the cloud service & hardware/it's a nextcloud instance; I own it, but it's very poorly secured; Proton owns it and their terms of use promise to not disclose it; OpenAI owns it and their terms of use say they can make use of my data)
Your initial „name one“ comment sounded like you didn’t believe there would be a jurisdiction where it is illegal.
My family members all back up our conversations to Google Drive, I doubt WhatsApp would provide that feature if it were illegal.
But if they use your input as training data, that would probably be enough.
My German isn't good enough to read the original text about this case, but if the sentiment behind https://natlawreview.com/article/data-mining-ai-systems-trai... is correct, I wouldn't be surprised if this would also fall under some kind of legal exception.
The biggest problem, of course, is that regardless of legality, this software will probably be used (and probably already is being used) because it's almost impossible to prove or disprove its use as a remote party.