Lightroom Sync does not stat when LrC is launched

After I have upgraded LrC to version 13 I see a strange behaviour quite often (but not always) when starting LrC: even if the cloud sign in the upper right corner is showing a green tick and stating "Synced" when clicking on it it doesn't start syncing when I change a photo in an already synced collection. In addition the double arrow symbol left to the collections showing if a collection is synced with the cloud or not is just missing. Also in the context menu of a collection (be it synced from before or not) the item "Sync with Lightroom" is missing.

Anyhow I can see my synced images under "All Synced Photographs" in the "Catalog" section and when I select "Synced Collections" in the collection filter it shows the collections having been synced from before.

As said, this doesn't happen each time when launching LrC but maybe 3 out of 4 times. Sometimes it helps to toggle "Pause Syncing" off and on again, sometimes it doesn't and I have to restart LrC, which helps most of the times.

Has anybody seen this behaviour, too?

Versions:
Lightroom Classic 13.0.1

MacOS Sonoma 14.1.1 (but same experience already with MacOS 13)