It is working correctly after all. I guess my memory was playing tricks on me. It only happens with test posts, not with real automated deliveries. There is no issue after all. My apologies.
Thanks for the reply, Michael. It has been happening for real automated deliveries. It has never worked as expected, but I only recently decided to delve into the issue.
I forgot to mention that I checked under the “Automated” tab of the Last Posts block and ensured that “Use the last newsletter date” and “Include only new posts” are selected.