I find that LLM extremely good in training such language skills by using following process:

a) write a draft yourself.

b) ask the LLM to correct your draft and make it better.

c) newer LLMs will explicitly mention the things they corrected (otherwise ask for being explict about the changes)

d) walk through each of the changes and apply the ones you feel that make the text better

This helped me improving my writing skills drastically (in multiple languages) compared to the times where I didn't have access to LLMs.