True, but Shazam is a testament to what's achievable even without audio source separation. Even going back about 10 years when I first tried it, I was kind of stupefied that it managed to work in a noisy department store.

But in some sense Shazam has it very easy - it is working from a discrete set of specific audio recordings, not, say, the set of artists, or the set of songs. Shazam is useless for live performances, or covers (by different band) of songs (unless those specific recordings are also in Shazam's database). Birdnet is tackling the problem of trying to get some essential properties of one species' song (and each bird is a new live performance, by a different cover artist).

There used to be an an app called Midomi (I think?) that could identify songs by humming or you singing, which was cool, but then I vaguely remember it rebranding itself and being less useful. Does anyone else know of a song-recognition app that is more like BirdNet and less like Shazam?

Google assistant does this. You can hum a song, or sing and it will recognize it with decent accuracy. Though humming camp town races lead me to this gem... https://www.youtube.com/watch?v=QFFykQIrPCk

Never heard of Midomi, but your description reminds me of Soundhound