It's hard for me to imagine they'd do something special to support "millions of songs" while excluding others, since the entire catalog is ~100m songs.

My guess is that it's entirely dynamic. It's hard to imagine the complexity of doing batch processing to render each song in the library, and maintain that as new songs are uploaded, and update the renders for software improvements. Better to just do it realtime.

And since classical, instrumentals, esoteric ambient stuff, death metal, etc, will probably not be supported by the algorithms, I think the "millions" refers to those that can be processed in realtime.

They do something special: get the necessary sign offs from legal. Apple‘s license for some content may bar it from being used that way (that’s another reason for doing it on device: could be different situation as far legal & licensing are concerned)

Sure, and a good point. I should have said they wouldn't do anything special on a song-by-song basis for millions of songs. It's not like someone's pushing the button for each song, or building a list of songs. Those that meet the criteria will be included, whether that is 10 or 10 million of them.

I’d guess it’s more probable that lots of songs simply have no lyrics at all, so the claim „all songs in the Apple Music catalog“ would be factually wrong.