any system that communicates information is apparently a digital communications system, so long as you can imagine an arbitrary scheme to interpret at least one bit of information from the signal,

This has always been my point since the beginning! There exist very low bandwidth digital communication systems in real life, with less than one bit per second. The bandwidth available should be defined where something is digital or not.

regardless of whether that was the message intended to be communicated.

Seeing the bird in the spectrogram is quite intentional and sufficient to consider this a communications system.

It seems if instead of a bird picture, a random set of bits were encoded and then detected In the spectrogram, you’d consider this more of a digital system since instead of a human doing the check you use an algorithm?