I think changing the name and general "stated goal" (AI powered CBT) would go a long way toward reducing confusion and improving outcomes/expectations. Cognitive-behavioral journaling might be a step closer to what you're actually doing and a step away from having handed someone in a very fragile state the tools to worsen that state (whether that is your goal or not).
In particular I'm reminded that people like Blake Lemoyne exist, who struggle far more than I or the typical HN'er when it comes to understanding that these LLM's are indeed very much _not_ alive, thinking, sentient, emotional, whatever. Someone who is experiencing delusional thinking already may actually be advised to go nowhere near an LLM, in much the same way we now know that social media can actively harm one's mental health.
Mostly I think people can and will use tools like this because it's their right to. I just think the "pitch" (I know you aren't monetizing) is strange and risky.
To your point about those who can't afford therapy - I don't see how that justifies participation with an experimental tool simply because it is cheaper. Even if you were a qualified health professional (there are many trying to make these type of apps), you really do need to go through the red tape that is government oversight and consensus within the field of psychiatry. This will take years.