I’m not aware of any paper about this; specially with how recent LLMs are, it’s kind of hard to detect tendencies.

That said, if I had to take a guess, the impact of LLMs in language will be rather subtle:

• Some words will become more common because bots use them a lot, and people become more aware of those words. “Delve” comes to my mind. (Urgh. I hate this word.)
• Swearing will become more common too. I wouldn’t be surprised if we saw an uptick of “fuck” and “shit” after ChatGPT was released. That’s because those bot don’t swear, so swearing is a good way to show “I’m human”.
• Idiosyncratic language might also increase, as a mix of the above and to avoid sounding “bland and bot-like”. Including letting some small typos to go through on purpose.

Text-to-speech, mentioned by @Shelbyeileen@lemmy.world, is another can of worms; it might reinforce non-common pronunciations until they become common. This should not be a big issue e.g. in Italian (that uses a mostly regular spelling), but it might be noticeable in English.