Done this as well. But after the initial "wow!" moment, the "make it better" part became a "actually I don't like how you wrote it, it doesn't sound like me".
There is a thin line between enhancing and taking over, and IMO the current LLMs cross it most of the time.
Your mistake was having the AI rewrite at all, don't do that, that is exactly the problem with them - that is them thinking for you. Ask the AI how well you wrote it, make the AI a writing professor, make the AI adopt a Socratic attitude that does not do anything but draws you to make the connection yourself.
I use Grammarly sometimes to check my more serious texts, but there's a gotcha. If you allow all of its stylistic choices, your writing becomes very sterile and devoid of any soul.
Your word and structural choices adds a flair of its own, makes something truly yours and unique. Don't let the tool kill that.
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.