I don't know what steps they can take. I suppose the best course of action is to deactivate the account if the LLM deems the user mentally unwell. Although that is just additional guardrails that could hurt the quality of the LLM.
I would absolutely not consider this overreaching if the statement within this thread that "it had referred the user to mental help hotlines multiple times in the past" is true.
That reaches near the fact that a lot of AI is not ready for the enterprise especially when interconnected with other AI agents since it lacks identity and privileged access management.
Perhaps one could establish the laws of "being able to use AI for what it is", for instance, within the boundary of the general public's web interface, not limiting the instances where it successfully advertises itself as "being unable to provide medical advice" or "is prone to or can make mistake", and such, to validating that the person understands by asking them directly and perhaps somewhat obviously indirectly and judging if they're aware that this is a computer you're talking to.
At some point they have to say "if we can't make this safe we can't do it at all". LLMs are great for some things, but if they will do this type of thing even once then they are not worth the gains and should be shutdown.
In any serious engineering operation, a failure like this is time to shut down everything and redesign until the same failure cannot happen. We all read Feynman's essay on Challenger right? But these companies want credit when their products work as advertised, but push the blame on users when they emit plausible lies or demonic advice. Taken too far that leads the police walking into HQ, arresting the board of directors, and selling the company for scrap. Just as often that leads to strict regulation so you can't be a cowboy coder or turn any loft into a sweatshop any more.