Messages not showing up in "Apps on this Mac using iCloud"

On my iPhone 6s the Messages has been enabled to be accessed via iCloud :

Screenshot of the iCloud screen on an iPhone

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 :

Screenshot of the top-half of Apps on this Mac using iCloud window on macOS

Screenshot of the bottom-half of Apps on this Mac using iCloud window on macOS

In addition "Text Message Forwarding" to that mac is enabled on the iPhone settings:

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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


For whatever reason, Apple decided some apps should use System Preferences to control their iCloud syncing and others should it themselves. For Messages (and FaceTime) on the Mac, iCloud sync settings are located within the app's preferences, where you are given the option to Enable messages in iCloud and to Sync Now. This is the Mac equivalent to what you've done on your iPhone.

iMessage Preferences Pane