Messages in iCloud don't sync anymore
I have switched on Messages in iCloud on all my devices. And as expected, after the initial setup, all messages are synced across all devices. Looked great.
However, after the setup of iCloud and initial sync, I have received a text message on my iPhone. But this simple text message (SMS) does not show up in iMessage on my Mac, even if I press Sync Now in the settings of iMessage on my Mac. (I have not switched on text forwarding in the iMessage settings on my iPhone as I believe the iCloud sync should take care of the syncing, and it has done so on the initial sync. All SMS messages have been synced.) I have already tried to sign out/sign in again to iCloud on the Mac, no luck.
Is there there some misunderstanding on my side how all this is supposed to work, or is something not working? Thanks for your help.
iPhone 8, 12