How do I download my text messages stored in iCloud

Apple mentions no direct way to access, view and download messages stored in iCloud.

However, if you reset your phone - and restore from iCloud backup, you will get your phone to how it was when the last iCloud backup was created - and in so doing, your messages which were on the phone at the time of the backup, will also be restored.

I do not recommend this method, because it most likely involves a possibility of some data loss - you can lose the data that has been put on the iPhone since the last backup.

I'm sorry, I do not understand what you are trying to accomplish and what you mean by, "separate syncing"! Please explain further should you need any assistance.

Device or computer? Have you tried signing out of Messages, restarting, and then signing back in to see if that will activate the sync?