On my iPhone 6s the Messages has been enabled to be accessed via iCloud :
Then I logged out of/back into my AppleId on the MacBook Pro with Big Sur. But the Messages still does not show up in Apps on this Mac using iCloud under System Preferences > iCloud :
In addition "Text Message Forwarding" to that mac is enabled on the iPhone settings:
What else needs to be done?
Update Messages that are created on the Mac are being correctly synced /viewable on the iPhone. But messages originating on the iPhone are not synced/visible on the Mac