Azure Storage Explorer - Not showing "failed" queue items?

Please note that Azure Storage Explorer is using Peek Messages API to show messages in a queue:

This operation retrieves one or more messages from the front of the queue, but does not alter the visibility of the message.

However, while Azure Function is processing the messages, it's using Get Messages API which makes the messages invisible to other consumers for a while:

The message is not automatically deleted from the queue, but after it has been retrieved, it is not visible to other clients for the time interval specified by the visibilitytimeout parameter.

Typically, when a consumer retrieves a message via Get Messages, that message is usually reserved for deletion until the visibilitytimeout interval expires, but this behavior is not guaranteed. After the visibilitytimeout interval expires, the message again becomes visible to other consumers. If the message is not subsequently retrieved and deleted by another consumer, the original consumer can delete the message using the original pop receipt.

In conclusion, if your messages weren't deleted by Azure Function (I guess it's the case per "Showing 0 of 3 messages in queue" message), you'll be able to see them after visibilitytimeout.