Are companies that have chats or similar Offer, obliged to delete messages at the author's request?

I would have a question about the legal situation with online chats, Massenger or e.g. Playstation (Sony) or X-BOX (Microsoft). If I start a chat with someone, it is then the duty of the provider to remove / delete messages at the request of the author (me), provided there's no delete function that enables the author to delete the message himself. If there's a legal regulation, I ask you to comment on these + paragraphs.

No they are not. In any case, not unconditionally. Only yesterday there was a new judgment from the BVG. In addition, in chat, the participant voluntarily expressed his opinion. So this is not data collected about him, but information provided by him.