I'm working on a Mac with Illustrator version 29.0. Even with a new document, after making changes, when I save I always get this message. I don't understand.
Could you confirm if the folder location you're saving to is synced via iCloud Drive/Dropbox or any other service? Also, could you try re-enabling Full Disk access for Illustrator (https://adobe.ly/45EchSU) and checking if it helps?