No conceivable harm in what sense? It seems obvious that it is harmful for a user who requests and is granted privacy to then have their private messages delivered to NYT. Legally it may be on shakier ground from the individual's perspective, but OpenAI argues that the harm is to their relationship with their customers and various governments, as well as the cost of the implementation effort:
>For OpenAI, risks of breaching its own privacy agreements could not only "damage" relationships with users but could also risk putting the company in breach of contracts and global privacy regulations. Further, the order imposes "significant" burdens on OpenAI, supposedly forcing the ChatGPT maker to dedicate months of engineering hours at substantial costs to comply, OpenAI claimed. It follows then that OpenAI's potential for harm "far outweighs News Plaintiffs’ speculative need for such data," OpenAI argued.
>> It seems obvious that it is harmful for a user who requests and is granted privacy to then have their private messages delivered to NYT.
This ruling is about preservation of evidence, not (yet) about delivering that information to one of the parties.
If judges couldn't compel parties to preserve evidence in active cases, you could see pretty easily that parties would aggressively destroy evidence that might be harmful to them at trial.
There's a whole later process (and probably arguments in front of the judge) about which evidence is actually delivered, whether it goes to the NYT or just to their lawyers, how much of it is redacted or anonymized, etc.