I just stumbled on this post late at night, so sorry if this is incoherent. I don't know if it's even possible, but I would love to see a catalogue that categorises rhythm games based on how they feel to play. I used to play Love Live, and on the expert and master maps, the rhythms don't really fit the tune of the song: they mostly lay down their own beat, and every time you click there's a little tambourine sound, so it really feels like playing percussion along to the song. This is very different to something like project sekai, where the flow of the map mostly traces the main tune. And it's different again to hard rhythm games like geometry dash and a dance of fire and ice, where the song is specifically designed to trip you up, and you have to memorise every twist and turn, so it's really satisfying when you do.
I have no idea what categories would be useful to other people, but I'd love to use a list with keywords that described the "game feel" to find new rhythm games!