messages does not show in list to back-up

If you mean settings - your name - icloud - those apps or data you're syncing with icloud.

Text, MMS and imessage is part of the icloud back up read here What does iCloud back up? - Apple Support

But if you're using this is it not and you're only syncing to icloud Keep all your messages in iCloud - Apple Support

Perhaps you have enabled "syncing messages" in Settings>[your name]>iCloud>Messages.

Should be this case, they are not included in your iCloud backup.

Regards

Giulio