[Hoping this might save someone some time.]

The code below stopped working when moving to the newer QueueClient class (in Azure.Storage.Queues) from the deprecated CloudQueue class (in Microsoft.Azure.Storage.Queue):

QueueClient queue = new QueueClient(accountConnectionString, "myQueuename");
queue.Create();
queue.SendMessage(msg);

Messages are being moved into the associated poison message queue, and I don't see any error messages in Azure's ApplicationInsights.

When I manually move the message in Azure Storage Explorer from the poison message queue back into the queue, it works!