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.
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.
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.