As someone else said, we don't know for sure. But it's not like there aren't some at-least-kinda-plausible candidate harms. Here are a few off the top of my head.

(By way of reminder, the question here is about the harms of LLMs specifically to the people using them, so I'm going to ignore e.g. people losing their jobs because their bosses thought an LLM could replace them, possible environmental costs, having the world eaten by superintelligent AI systems that don't need humans any more, use of LLMs to autogenerate terrorist propaganda or scam emails, etc.)

People become like those they spend time with. If a lot of people are spending a lot of time with LLMs, they are going to become more like those LLMs. Maybe only in superficial ways (perhaps they increase their use of the word "delve" or the em-dash or "it's not just X, it's Y" constructions), maybe in deeper ways (perhaps they adapt their _personalities_ to be more like the ones presented by the LLMs). In an individual isolated case, this might be good or bad. When it happens to _everyone_ it makes everyone just a bit more similar to one another, which feels like probably a bad thing.

Much of the point of an LLM as opposed to, say, a search engine is that you're outsourcing not just some of your remembering but some of your thinking. Perhaps widespread use of LLMs will make people mentally lazier. People are already mostly very lazy mentally. This might be bad for society.

People tend to believe what LLMs tell them. LLMs are not perfectly reliable. Again, in isolation this isn't particularly alarming. (People aren't perfectly reliable either. I'm sure everyone reading this believes at least one untrue thing that they believe because some other person said it confidently.) But, again, when large swathes of the population are talking to the same LLMs which make the same mistakes, that could be pretty bad.

Everything in the universe tends to turn into advertising under the influence of present-day market forces. There are less-alarming ways for that to happen with LLMs (maybe they start serving ads in a sidebar or something) and more-alarming ways: maybe companies start paying OpenAI to manipulate their models' output in ways favourable to them. I believe that in many jurisdictions "subliminal advertising" in movies and television is illegal; I believe it's controversial whether it actually works. But I suspect something similar could be done with LLMs: find things associated with your company and train the LLM to mention them more often and with more positive associations. If it can be done, there's a good chance that eventually it will be. Ewww.

All the most capable LLMs run in the cloud. Perhaps people will grow dependent on them, and then the companies providing them -- which are, after all, mostly highly unprofitable right now -- decide to raise their prices massively, to a point at which no one would have chosen to use them so much at the outset. (But at which, having grown dependent on the LLMs, they continue using them.)