Can old deleted iMessage threads be restored setting up a new Apple device?
The thread you posted and information are from 2013. Old information relevant for older iOS versions. If you restore from an iCloud backup, messages are restored to the device.

With the latest iOS, you can also backup iMessages to iCloud separately from an iCloud backup. Now you can save iMessages to iCloud, but it's a feature that you have to enable separately through settings.

Go to Settings app → Apple ID → iCloud → Messages and enable the switch. You can also back up to iTunes to save/restore that kind of data. If you do not have the Messages in iCloud feature enabled and/or do not restore from an iTunes/iCloud backup, no iMessages will be restored to the device.

Here are a couple related Apple Support documents for reference:


Keep all your messages in iCloud
About backups for iOS devices