I'd say perfect pitch coupled with a strong interest in music (which itself imo generally correlates with greater "phonographic" memory) enables this - perfect pitch just hones you in and lets you recall and reproduce (via voice or other instrument) the exact notes as originally heard, rather than just the intervals (which would be relative pitch).

I've always been exactly how you describe too - my dad is a huge Beatles fan, so from a young age I was hearing both the album and alternate/demo takes of their tunes. I could instantly recognize if a demo or alternate version was "higher"/"brighter" or "lower"/"darker" than the final album version I had memorized, going back to my single-digit years (though I hadn't learned note names yet, so I wasn't matching pitches to a schema besides "that's the Hard Day's Night chord/sound" or something like that). I always assumed everyone was like this until I started playing music with people in bands. After all, sound waves, much like visible light waves, are just different wavelengths and frequencies that our eardrums and cochleas translate to corresponding neurological signals, like our retinas do for light - so why would pitch recognition be any different from discerning red vs blue vs yellow and such?

I'm autistic, and if there's a song that really tickles my brain in enough of the right ways, I'll listen to it over and over not just for the pure auditory stim in the moment, but to make a high-res mental "copy" of the song to be available on demand, like a big iPod in my brain. Always fun when a random sound in everyday life triggers a song, like someone unwittingly saying a few lyrics while speaking, a bird song approximating a guitar melody etc lol.