Have had the same issue for some time. Have tried with Mac OS Mojave and Big Sur with LibreOffice 7.1.5.2 and 7.2.0.4. Duplicate labels on each sheet - so 20 labels gives me 20 sheets instead of 20 individual labels.
Followed the Mail Merge instructions precisely from the documentation. Unfortunately I haven’t been able to work out when this feature got broken.
As mentioned, you have deleted the “Next Record” marker from the first label, and then synced labels. However, you can solve this without creating a new document. Insert → Field → Next Record and click Insert. Brackets are inserted [] and this will correct the issue.