Fun post but SoundHound has done this pretty much flawlessly for 10 years. It's also built-in in Google Search and on all Android phones. In that context "Shazam for Singing" is an unfortunate title since it implies nothing like that exist and that Shazam is SOTA, when it's the other way around.

No idea how Shazam can be so far behind and still be synonymous with song identification in everyday speech.