My guess is that a statistical analysis of other things such as access patterns, timestamps, content you engage with, etc, could de-anonymize you regardless of the phrasing you use, so LLMs won't save you.
True, but you could also use llms to autonomously engage with content you're not interested in, batch replies for times you're not around, inject coherent, consistent, plausible, but false details into your messages, or modify/flag details you didn't mean to disclose.