I contacted Apple Support about this, spent an hour on the phone. The only way to get the sync back working was to create a new Photos library on the Mac and discard the old one. Fortunately no data appears to be lost.
What was also found out is that according to support, this statement from the Apple support article and my original question, isn't actually true.
"And when you have iCloud Photos turned on, the people you favorite or name stay up to date across your Apple devices."
The People/faces stay up to date across iOS devices only. Apparently, but even Apple support couldn't say exactly, on MacOS the facial recognition is more in-device. Some metadata is still shared, since for example the favourite people on the People folder do sync to the Mac. But it's all not really on 1-to-1.
Lessons learned
1) don't trust marketing speeches
2) rely on Apple Support (usually free)
Hoping this issue will be fixed down the road.