The journey to a magical, free bird sound ID app involves some obvious steps (the NSF gave them money), but the amount of timeline offramps is really high. The NSF didn't think this app was educational ("it's just telling them the answer, they don't even have to work for it!"), the funding ran out so they were thinking of charging money, eBird happened to have five years of bird sound recordings they could use, a computer vision guy on the team happened to learn that spectrograms are basically the same as pictures...
And the result is tremendously useful! They get great signal on where birds are, and they're making people so much more interested in birds and nature and science. And I think charging $1 for the app or, shudder, some sort of subscription model might've ruined the whole thing.
Personal best for a single session is 23 birds in my back garden over the course of a couple of coffees. I have though spent a fair bit of time making the garden as attractive to different types of bird as possible - mainly through having a variety of different shaped feeders with different feed in. I can recommend the NatureSpy camera feeder too [0] - though I have had to modify it a little to make the food hole smaller otherwise magpies empty the thing in a single day just chucking all the seed on the floor. Dickheads.
[0] https://naturespy.org/collections/wifi-solar-bird-feeder-nes...
Unless a species has a really, really unique call or song, I've made it my personal rule to get eyes on it and, if I'm still not convinced, to take a picture and cross reference with iNaturalist and what folks on there think of it.
I've learned to curse the species that differ from others by the sheen of the backs of the males' necks or the angle of a wingbar. Also, gulls that only differ by things like the color of their feet or beaks.
Given that it's colloquially “Shazam for birds” and Shazam is just amazingly resistant to noise, it's a bit disappointing :-)
Merlin is solving the more general problem so makes sense that it's much more finicky and less accurate.
YouTube Music and Google Search do OK with these types. Sometimes if I know a song well enough, I will open YT Music, activate the mic search, and sing a few bars, instead of typing the song title.
According to Gemini, SoundHound is also a good app for song-hummers to try.
Shazam primarily identifies on the geometry of spectogram peaks, FWIW (I wrote my master's thesis on the DSP of music recognition back in the day; it's possible that they are doing something more fancy now, of course, but I'm not sure if they would want to). I don't know exactly what Merlin is doing.